Renormalization Group Functional Equations
Curtright, Thomas L
2011-01-01
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories. With minimal assumptions, the methods produce continuous flows from step-scaling {\\sigma} functions, and lead to exact functional relations for the local flow {\\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.
Compositeness condition in the renormalization group equation
International Nuclear Information System (INIS)
Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko
1990-01-01
The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)
Exact renormalization group equations: an introductory review
Bagnuls, C.; Bervillier, C.
2001-07-01
We critically review the use of the exact renormalization group equations (ERGE) in the framework of the scalar theory. We lay emphasis on the existence of different versions of the ERGE and on an approximation method to solve it: the derivative expansion. The leading order of this expansion appears as an excellent textbook example to underline the nonperturbative features of the Wilson renormalization group theory. We limit ourselves to the consideration of the scalar field (this is why it is an introductory review) but the reader will find (at the end of the review) a set of references to existing studies on more complex systems.
Quarkonia from charmonium and renormalization group equations
International Nuclear Information System (INIS)
Ditsas, P.; McDougall, N.A.; Moorhouse, R.G.
1978-01-01
A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters αsub(s) are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit Hamiltonian for obtaining the charmonium hyperfine splitting is criticized. (Auth.)
Covariant Derivatives and the Renormalization Group Equation
Dolan, Brian P.
The renormalization group equation for N-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has components given by the β functions of the theory. It is argued that this simple picture requires modification whenever any one of the points at which the amplitude is evaluated becomes close to any other. This modification necessitates the introduction of a connection on the space of couplings and new terms appear in the renormalization group equation involving covariant derivatives of the β function and the curvature associated with the connection. It is shown how the connection is related to the operator product expansion coefficients, but there remains an arbitrariness in its definition.
Renormalization group equations with multiple coupling constants
International Nuclear Information System (INIS)
Ghika, G.; Visinescu, M.
1975-01-01
The main purpose of this paper is to study the renormalization group equations of a renormalizable field theory with multiple coupling constants. A method for the investigation of the asymptotic stability is presented. This method is applied to a gauge theory with Yukawa and self-quartic couplings of scalar mesons in order to find the domains of asymptotic freedom. An asymptotic expansion for the solutions which tend to the origin of the coupling constants is given
On the renormalization group equations of quantum electrodynamics
International Nuclear Information System (INIS)
Hirayama, Minoru
1980-01-01
The renormalization group equations of quantum electrodynamics are discussed. The solution of the Gell-Mann-Low equation is presented in a convenient form. The interrelation between the Nishijima-Tomozawa equation and the Gell-Mann-Low equation is clarified. The reciprocal effective charge, so to speak, turns out to play an important role to discuss renormalization group equations. Arguments are given that the reciprocal effective charge vanishes as the renormalization momentum tends to infinity. (author)
Zeta Functions, Renormalization Group Equations, and the Effective Action
International Nuclear Information System (INIS)
Hochberg, D.; Perez-Mercader, J.; Molina-Paris, C.; Visser, M.
1998-01-01
We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley-DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action and use this to derive the leading logarithms in the one-loop effective action for arbitrary quantum field theories. copyright 1998 The American Physical Society
Generalized Callan-Symanzik equations and the Renormalization Group
International Nuclear Information System (INIS)
MacDowell, S.W.
1975-01-01
A set of generalized Callan-Symanzik equations derived by Symanzik, relating Green's functions with arbitrary number of mass insertions, is shown be equivalent to the new Renormalization Group equation proposed by S. Weinberg
String field equation from renormalization group
International Nuclear Information System (INIS)
Sakai, Kenji.
1988-10-01
We derive an equation of motion for an open bosonic string field which is introduced as a background field in a sigma model. By using the method of Klebanov and Susskind, we obtain the β-function for this background field and investigate its properties. (author)
Renormalization group equations in the stochastic quantization scheme
International Nuclear Information System (INIS)
Pugnetti, S.
1987-01-01
We show that there exists a remarkable link between the stochastic quantization and the theory of critical phenomena and dynamical statistical systems. In the stochastic quantization of a field theory, the stochastic Green functions coverge to the quantum ones when the frictious time goes to infinity. We therefore use the typical techniques of the Renormalization Group equations developed in the framework of critical phenomena to discuss some features of the convergence of the stochastic theory. We are also able, in this way, to compute some dynamical critical exponents and give new numerical valuations for them. (orig.)
Space-time versus world-sheet renormalization group equation in string theory
International Nuclear Information System (INIS)
Brustein, R.; Roland, K.
1991-05-01
We discuss the relation between space-time renormalization group equation for closed string field theory and world-sheet renormalization group equation for first-quantized strings. Restricting our attention to massless states we argue that there is a one-to-one correspondence between the fixed point solutions of the two renormalization group equations. In particular, we show how to extract the Fischler-Susskind mechanism from the string field theory equation in the case of the bosonic string. (orig.)
Automatic calculation of supersymmetric renormalization group equations and loop corrections
Staub, Florian
2011-03-01
SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. This information can be used by SARAH to write model files for CalcHep/ CompHep or FeynArts/ FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one- and two-loop level. Furthermore, it calculates the one-loop self-energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates. Program summaryProgram title: SARAH Catalogue identifier: AEIB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 97 577 No. of bytes in distributed program, including test data, etc.: 2 009 769 Distribution format: tar.gz Programming language: Mathematica Computer: All systems that Mathematica is available for Operating system: All systems that Mathematica is available for Classification: 11.1, 11.6 Nature of problem: A supersymmetric model is usually characterized by the particle content, the gauge sector and the superpotential. It is a time consuming process to obtain all necessary information for phenomenological studies from these basic ingredients. Solution method: SARAH calculates the complete Lagrangian for a given model whose
Exact renormalization group equation for the Lifshitz critical point
Bervillier, C.
2004-10-01
An exact renormalization equation (ERGE) accounting for an anisotropic scaling is derived. The critical and tricritical Lifshitz points are then studied at leading order of the derivative expansion which is shown to involve two differential equations. The resulting estimates of the Lifshitz critical exponents compare well with the O(ε) calculations. In the case of the Lifshitz tricritical point, it is shown that a marginally relevant coupling defies the perturbative approach since it actually makes the fixed point referred to in the previous perturbative calculations O(ε) finally unstable.
Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.
Saveliev, V L; Gorokhovski, M A
2005-07-01
On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.
Nonperturbative renormalization group study of the stochastic Navier-Stokes equation.
Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-07-01
We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4-2ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's -5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the -5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.
Renormalization group and asymptotic freedom
International Nuclear Information System (INIS)
Morris, J.R.
1978-01-01
Several field theoretic models are presented which allow exact expressions of the renormalization constants and renormalized coupling constants. These models are analyzed as to their content of asymptotic free field behavior through the use of the Callan-Symanzik renormalization group equation. It is found that none of these models possesses asymptotic freedom in four dimensions
Quantum master equation for QED in exact renormalization group
International Nuclear Information System (INIS)
Igarashi, Yuji; Itoh, Katsumi; Sonoda, Hidenori
2007-01-01
Recently, one of us (H. S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the nilpotency of the BRS transformation is lost. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action. (author)
PyR@TE. Renormalization group equations for general gauge theories
Lyonnet, F.; Schienbein, I.; Staub, F.; Wingerter, A.
2014-03-01
Although the two-loop renormalization group equations for a general gauge field theory have been known for quite some time, deriving them for specific models has often been difficult in practice. This is mainly due to the fact that, albeit straightforward, the involved calculations are quite long, tedious and prone to error. The present work is an attempt to facilitate the practical use of the renormalization group equations in model building. To that end, we have developed two completely independent sets of programs written in Python and Mathematica, respectively. The Mathematica scripts will be part of an upcoming release of SARAH 4. The present article describes the collection of Python routines that we dubbed PyR@TE which is an acronym for “Python Renormalization group equations At Two-loop for Everyone”. In PyR@TE, once the user specifies the gauge group and the particle content of the model, the routines automatically generate the full two-loop renormalization group equations for all (dimensionless and dimensionful) parameters. The results can optionally be exported to LaTeX and Mathematica, or stored in a Python data structure for further processing by other programs. For ease of use, we have implemented an interactive mode for PyR@TE in form of an IPython Notebook. As a first application, we have generated with PyR@TE the renormalization group equations for several non-supersymmetric extensions of the Standard Model and found some discrepancies with the existing literature. Catalogue identifier: AERV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERV_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 924959 No. of bytes in distributed program, including test data, etc.: 495197 Distribution format: tar.gz Programming language: Python. Computer
Traveling waves and the renormalization group improvedBalitsky-Kovchegov equation
Energy Technology Data Exchange (ETDEWEB)
Enberg, Rikard
2006-12-01
I study the incorporation of renormalization group (RG)improved BFKL kernels in the Balitsky-Kovchegov (BK) equation whichdescribes parton saturation. The RG improvement takes into accountimportant parts of the next-to-leading and higher order logarithmiccorrections to the kernel. The traveling wave front method for analyzingthe BK equation is generalized to deal with RG-resummed kernels,restricting to the interesting case of fixed QCD coupling. The resultsshow that the higher order corrections suppress the rapid increase of thesaturation scale with increasing rapidity. I also perform a "diffusive"differential equation approximation, which illustrates that someimportant qualitative properties of the kernel change when including RGcorrections.
A simple proof of renormalization group equation in the minimal subtraction scheme
International Nuclear Information System (INIS)
Chetyrkin, K.G.
1989-04-01
We give a simple combinatorial proof of the renormalization group equation in the minimal subtraction scheme. Being mathematically rigorous, the proof avoids both the notorious complexity of techniques using parametric representations of Feynman diagrams and heuristic arguments of usual ''proofs'' calling up bare fields living in the space-time of complex dimension. It also copes easily with the general case of Green functions of arbitrary number of composite fields. (author). 24 refs
Simple renormalization group method for calculating geometrical and other equations of states
International Nuclear Information System (INIS)
Tsallis, C.; Schwaccheim, G.; Coniglio, A.
1984-01-01
A real space renormalization group procedure to calculate geometrical and thermal equations of states for the entire range of values of the external parameters is described. Its use is as simple as a Mean Field Approximation; however, it yields non trivial results and can be systematically improved. Such a procedure is illustrated by calculating, for all bond concentrations, the site mass density for the complete and the backbone percolating infinite clusters in square lattice: the results are quite satisfactory. (Author) [pt
Exact CTP renormalization group equation for the coarse-grained effective action
International Nuclear Information System (INIS)
Dalvit, D.A.; Mazzitelli, F.D.
1996-01-01
We consider a scalar field theory in Minkowski spacetime and define a coarse-grained closed time path (CTP) effective action by integrating quantum fluctuations of wavelengths shorter than a critical value. We derive an exact CTP renormalization group equation for the dependence of the effective action on the coarse-graining scale. We solve this equation using a derivative expansion approach. Explicit calculation is performed for the λφ 4 theory. We discuss the relevance of the CTP average action in the study of nonequilibrium aspects of phase transitions in quantum field theory. copyright 1996 The American Physical Society
Renormalization Group Equations of d=6 Operators in the Standard Model Effective Field Theory
CERN. Geneva
2015-01-01
The one-loop renormalization group equations for the Standard Model (SM) Effective Field Theory (EFT) including dimension-six operators are calculated. The complete 2499 × 2499 one-loop anomalous dimension matrix of the d=6 Lagrangian is obtained, as well as the contribution of d=6 operators to the running of the parameters of the renormalizable SM Lagrangian. The presence of higher-dimension operators has implications for the flavor problem of the SM. An approximate holomorphy of the one-loop anomalous dimension matrix is found, even though the SM EFT is not a supersymmetric theory.
Singular solutions of renormalization group equations and the symmetry of the lagrangian
International Nuclear Information System (INIS)
Kazakov, D.I.; Shirokov, D.V.
1975-01-01
On the basis of solution of the differential renormalization group equations the method is proposed for finding out the Lagrangians possessing some king of internal symmetry. It is shown that in the phase space of the invariant charges the symmetry corresponds to the straight-line singular solution of these equations remaining straight-line when taking into account the higher order corrections. We have studied the model of scalar fields with quartic couplings, as well as the set of models containing scalar, pseudoscalar and spinor fields with Yukawa and quartic interactions. Straight-line singular solutions in the first case correspond to isotopic symmetry only. For the second case they correspond to supersymmetry. No other symmetries have been discovered. For the model containing the gauge fields the solution corresponding to supersymmetry is obtained and it is shown that this is also the only symmetry that can be realized in the given set of fields
Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene
International Nuclear Information System (INIS)
Ardenghi, J.S.; Bechthold, P.; Jasen, P.; Gonzalez, E.; Juan, A.
2014-01-01
The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response functions are derived and computed in the Boltzmann limit showing that in the former case a minimum conductivity appears in the no-disorder limit. In turn, from the generalization of both functions, an exact relation can be obtained that relates both. Combining this result with the relation given by the continuity equation it is possible to obtain general functional behavior of the diffusion pole. Finally, a dynamical diffusion is computed in the quasistatic limit using the definition of relaxation function. A lower cutoff must be introduced to regularize infrared divergences which allow us to obtain a full renormalization group equation for the Fermi velocity, which is solved up to order O(ℏ 2 )
Renormalization group equation for interacting Thirring fields in dimensional regularization scheme
International Nuclear Information System (INIS)
Chowdhury, A.R.; Roy, T.; Kar, S.
1976-01-01
The dynamics of two interacting Thirring fields has been investigated within the dimensional regularization framework. The coupling constants are renormalized in the same way as observed in the non-perturbative approach of Ansel'm et al (Sov. Phys. - JETP 36: 608 (1959)). Functionsβsub(i)(g 1 , g 2 , g 3 ) and γsub(i)(g 1 , g 2 , g 3 ), pertaining to the stability and anomalous behaviour of the problem, are computed up to a third order in the coupling parameters. With the help of these, subsidiary non-linear differential equations of the renormalization group are studied in 2-epsilon dimension. The results show up some peculiar features of the theory: a zero of βsub(i)(g 1 , g 2 , g 3 ) corresponding to g 2 approximately α√epsilon, a characteristic of phi theory. The scale invariant limit is reached when g 2 → 0 (i.e. the two Thirring fields are decoupled) and also when g 1 = xg 2 = g 3 , where x is a root of 2x 3 + 2x 2 - 1 = 0. The branch-point zero makes the transition to the epsilon tends to 0 limit non-unique. The anomalous dimensions are obtained and seen to match that of the Dashen-Frishman model (Phys. Lett.; 46B 439 (1973)). The existence of a non-trivial scale invariant limit distinguishes the model from many simple field theories. (author)
Probing the desert by the two-loop renormalization-group equations
International Nuclear Information System (INIS)
Tanimoto, M.; Suetake, Y.; Senba, K.
1987-01-01
We have reexamined the study of probing the desert with fermion masses, presented by Bagger, Dimopoulos, and Masso, by using the two-loop renormalization-group equations in the framework of the SU(3) x SU(2) x U(1) model with three generations and one Higgs doublet. The blow-up energy scale of the Yukawa coupling is found to be dependent on the Higgs quartic coupling λ. If the Yukawa coupling blows up between the electroweak scale M/sub W/ and the grand unified scale M/sub X/, the Higgs potential is destabilized for small values of λ at the electroweak scale M/sub W/, and becomes strongly coupled for large values of λ at M/sub W/. It is found that the Higgs-scalar mass as well as the fermion masses are important to probe the desert
DeVille, R. E. Lee; Harkin, Anthony; Holzer, Matt; Josić, Krešimir; Kaper, Tasso J.
2008-06-01
For singular perturbation problems, the renormalization group (RG) method of Chen, Goldenfeld, and Oono [Phys. Rev. E. 49 (1994) 4502-4511] has been shown to be an effective general approach for deriving reduced or amplitude equations that govern the long time dynamics of the system. It has been applied to a variety of problems traditionally analyzed using disparate methods, including the method of multiple scales, boundary layer theory, the WKBJ method, the Poincaré-Lindstedt method, the method of averaging, and others. In this article, we show how the RG method may be used to generate normal forms for large classes of ordinary differential equations. First, we apply the RG method to systems with autonomous perturbations, and we show that the reduced or amplitude equations generated by the RG method are equivalent to the classical Poincaré-Birkhoff normal forms for these systems up to and including terms of O(ɛ2), where ɛ is the perturbation parameter. This analysis establishes our approach and generalizes to higher order. Second, we apply the RG method to systems with nonautonomous perturbations, and we show that the reduced or amplitude equations so generated constitute time-asymptotic normal forms, which are based on KBM averages. Moreover, for both classes of problems, we show that the main coordinate changes are equivalent, up to translations between the spaces in which they are defined. In this manner, our results show that the RG method offers a new approach for deriving normal forms for nonautonomous systems, and it offers advantages since one can typically more readily identify resonant terms from naive perturbation expansions than from the nonautonomous vector fields themselves. Finally, we establish how well the solution to the RG equations approximates the solution of the original equations on time scales of O(1/ɛ).
Epelbaum, E.; Gegelia, J.; Meißner, Ulf-G.
2018-03-01
The Wilsonian renormalization group approach to the Lippmann-Schwinger equation with a multitude of cutoff parameters is introduced. A system of integro-differential equations for the cutoff-dependent potential is obtained. As an illustration, a perturbative solution of these equations with two cutoff parameters for a simple case of an S-wave low-energy potential in the form of a Taylor series in momenta is obtained. The relevance of the obtained results for the effective field theory approach to nucleon-nucleon scattering is discussed. Supported in part by BMBF under Grant No. 05P2015 - NUSTAR R&D), DFG and NSFC through Funds Provided to the Sino- German CRC 110 “Symmetries and the Emergence of Structure in QCD”, National Natural Science Foundation of China under Grant No. 11621131001, DFG Grant No. TRR110, the Georgian Shota Rustaveli National Science Foundation (grant FR/417/6-100/14) and the CAS President’s International Fellowship Initiative (PIFI) under Grant No. 2017VMA0025
Renormalization group in quantum mechanics
International Nuclear Information System (INIS)
Polony, J.
1996-01-01
The running coupling constants are introduced in quantum mechanics and their evolution is described with the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The Hamiltonian and the Lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models. Copyright copyright 1996 Academic Press, Inc
Renormalization-group equations of neutrino masses and flavor mixing parameters in matter
Xing, Zhi-zhong; Zhou, Shun; Zhou, Ye-Ling
2018-05-01
We borrow the general idea of renormalization-group equations (RGEs) to understand how neutrino masses and flavor mixing parameters evolve when neutrinos propagate in a medium, highlighting a meaningful possibility that the genuine flavor quantities in vacuum can be extrapolated from their matter-corrected counterparts to be measured in some realistic neutrino oscillation experiments. Taking the matter parameter a≡ 2√{2}{G}F{N}_eE to be an arbitrary scale-like variable with N e being the net electron number density and E being the neutrino beam energy, we derive a complete set of differential equations for the effective neutrino mixing matrix V and the effective neutrino masses {\\tilde{m}}_i (for i = 1 , 2 , 3). Given the standard parametrization of V , the RGEs for {{\\tilde{θ}}_{12}, {\\tilde{θ}}_{13}, {\\tilde{θ}}_{23}, \\tilde{δ}} in matter are formulated for the first time. We demonstrate some useful differential invariants which retain the same form from vacuum to matter, including the well-known Naumov and Toshev relations. The RGEs of the partial μ- τ asymmetries, the off-diagonal asymmetries and the sides of unitarity triangles of V are also obtained as a by-product.
International Nuclear Information System (INIS)
Stephens, C. R.
2006-01-01
In this article I give a brief account of the development of research in the Renormalization Group in Mexico, paying particular attention to novel conceptual and technical developments associated with the tool itself, rather than applications of standard Renormalization Group techniques. Some highlights include the development of new methods for understanding and analysing two extreme regimes of great interest in quantum field theory -- the ''high temperature'' regime and the Regge regime
Energy Technology Data Exchange (ETDEWEB)
Borchardt, Julia
2017-02-07
By means of the functional renormalization group (FRG), systems can be described in a nonperturbative way. The derived flow equations are solved via pseudo-spectral methods. As they allow to resolve the full field dependence of the effective potential and provide highly accurate results, these numerical methods are very powerful but have hardly been used in the FRG context. We show their benefits using several examples. Moreover, we apply the pseudo-spectral methods to explore the phase diagram of a bosonic model with two coupled order parameters and to clarify the nature of a possible metastability of the Higgs-Yukawa potential.In the phase diagram of systems with two competing order parameters, fixed points govern multicritical behavior. Such systems are often discussed in the context of condensed matter. Considering the phase diagram of the bosonic model between two and three dimensions, we discover additional fixed points besides the well-known ones from studies in three dimensions. Interestingly, our findings suggest that in certain regions of the phase diagram, two universality classes coexist. To our knowledge, this is the first bosonic model where coexisting (multi-)criticalities are found. Also, the absence of nontrivial fixed points can have a physical meaning, such as in the electroweak sector of the standard model which suffers from the triviality problem. The electroweak transition giving rise to the Higgs mechanism is dominated by the Gaussian fixed point. Due to the low Higgs mass, perturbative calculations suggest a metastable potential. However, the existence of the lower Higgs-mass bound eventually is interrelated with the maximal ultraviolet extension of the standard model. A relaxation of the lower bound would mean that the standard model may be still valid to even higher scales. Within a simple Higgs-Yukawa model, we discuss the origin of metastabilities and mechanisms, which relax the Higgs-mass bound, including higher field operators.
International Nuclear Information System (INIS)
Box, Andrew D.; Tata, Xerxes
2009-01-01
We reexamine the one-loop renormalization group equations (RGEs) for the dimensionful parameters of the minimal supersymmetric standard model (MSSM) with broken supersymmetry, allowing for arbitrary flavor structure of the soft SUSY-breaking parameters. We include threshold effects by evaluating the β-functions in a sequence of (nonsupersymmetric) effective theories with heavy particles decoupled at the scale of their mass. We present the most general form for high-scale, soft SUSY-breaking parameters that obtains if we assume that the supersymmetry-breaking mechanism does not introduce new intergenerational couplings. This form, possibly amended to allow additional sources of flavor-violation, serves as a boundary condition for solving the RGEs for the dimensionful MSSM parameters. We then present illustrative examples of numerical solutions to the RGEs. We find that in a SUSY grand unified theory with the scale of SUSY scalars split from that of gauginos and higgsinos, the gaugino mass unification condition may be violated by O(10%). As another illustration, we show that in mSUGRA, the rate for the flavor-violating t-tilde 1 →cZ-tilde 1 decay obtained using the complete RGE solution is smaller than that obtained using the commonly used 'single-step' integration of the RGEs by a factor 10-25, and so may qualitatively change expectations for topologies from top-squark pair production at colliders. Together with the RGEs for dimensionless couplings presented in a companion paper, the RGEs in Appendix 2 of this paper form a complete set of one-loop MSSM RGEs that include threshold and flavor-effects necessary for two-loop accuracy.
Introduction to the functional renormalization group
International Nuclear Information System (INIS)
Kopietz, Peter; Bartosch, Lorenz; Schuetz, Florian
2010-01-01
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics. (orig.)
International Nuclear Information System (INIS)
Busa, J.; Ajryan, Eh.A.; Jurcisinova, E.; Jurcisin, M.; Remecky, R.
2009-01-01
Using the field-theoretic renormalization group, the influence of strong uniaxial small-scale anisotropy on the stability of inertial-range scaling regimes in a model of passive transverse vector field advected by an incompressible turbulent flow is investigated. The velocity field is taken to have a Gaussian statistics with zero mean and defined noise with finite time correlations. It is shown that the inertial-range scaling regimes are given by the existence of infrared stable fixed points of the corresponding renormalization group equations with some angle integrals. The analysis of integrals is given. The problem is solved numerically and the borderline spatial dimension d e (1,3] below which the stability of the scaling regime is not present is found as a function of anisotropy parameters
Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory
International Nuclear Information System (INIS)
Chen, G.-H.; Wu, Y.-S.
2002-01-01
A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level
The analytic renormalization group
Directory of Open Access Journals (Sweden)
Frank Ferrari
2016-08-01
Full Text Available Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients Gk, k∈Z, associated with the Matsubara frequencies νk=2πk/β. We show that analyticity implies that the coefficients Gk must satisfy an infinite number of model-independent linear equations that we write down explicitly. In particular, we construct “Analytic Renormalization Group” linear maps Aμ which, for any choice of cut-off μ, allow to express the low energy Fourier coefficients for |νk|<μ (with the possible exception of the zero mode G0, together with the real-time correlators and spectral functions, in terms of the high energy Fourier coefficients for |νk|≥μ. Operating a simple numerical algorithm, we show that the exact universal linear constraints on Gk can be used to systematically improve any random approximate data set obtained, for example, from Monte-Carlo simulations. Our results are illustrated on several explicit examples.
International Nuclear Information System (INIS)
Antonov, N.V.; Borisenok, S.V.; Girina, V.I.
1996-01-01
Within the framework of the renormalization group approach to the theory of fully developed turbulence we consider the problem of possible IR relevant corrections to the Navier-Stokes equation. We formulate an exact criterion of the actual IR relevance of the corrections. In accordance with this criterion we verify the IR relevance for certain classes of composite operators. 17 refs., 2 tabs
International Nuclear Information System (INIS)
Daum, Jan-Eric
2011-01-01
Whereas the Standard Model of elementary particle physics represents a consistent, renormalizable quantum field theory of three of the four known interactions, the quantization of gravity still remains an unsolved problem. However, in recent years evidence for the asymptotic safety of gravity was provided. That means that also for gravity a quantum field theory can be constructed that is renormalizable in a generalized way which does not explicitly refer to perturbation theory. In addition, this approach, that is based on the Wilsonian renormalization group, predicts the correct microscopic action of the theory. In the classical framework, metric gravity is equivalent to the Einstein-Cartan theory on the level of the vacuum field equations. The latter uses the tetrad e and the spin connection ω as fundamental variables. However, this theory possesses more degrees of freedom, a larger gauge group, and its associated action is of first order. All these features make a treatment analogue to metric gravity much more difficult. In this thesis a three-dimensional truncation of the form of a generalized Hilbert-Palatini action is analyzed. Besides the running of Newton's constant G k and the cosmological constant Λ k , it also captures the renormalization of the Immirzi parameter γ k . In spite of the mentioned difficulties, the spectrum of the free Hilbert-Palatini propagator can be computed analytically. On its basis, a proper time-like flow equation is constructed. Furthermore, appropriate gauge conditions are chosen and analyzed in detail. This demands a covariantization of the gauge transformations. The resulting flow is analyzed for different regularization schemes and gauge parameters. The results provide convincing evidence for asymptotic safety within the (e,ω) approach as well and therefore for the possible existence of a mathematically consistent and predictive fundamental quantum theory of gravity. In particular, one finds a pair of non-Gaussian fixed
Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization
International Nuclear Information System (INIS)
Ohta, Nobuyoshi; Percacci, Roberto; Vacca, Gian Paolo
2016-01-01
We employ the exponential parametrization of the metric and a ''physical'' gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. (orig.)
Renormalization group in modern physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1988-01-01
Renormalization groups used in diverse fields of theoretical physics are considered. The discussion is based upon functional formulation of group transformations. This attitude enables development of a general method by using the notion of functional self-similarity which generalizes the usual self-similarity connected with power similarity laws. From this point of view the authors present a simple derivation of the renorm-group (RG) in QFT liberated from ultra-violet divergences philosophy, discuss the RG approach in other fields of physics and compare different RG's
Unambiguity of renormalization group calculations in QCD
International Nuclear Information System (INIS)
Vladimirov, A.A.
1979-01-01
A detailed analysis of the reduction of ambiguities determined by an arbitrary renormalization scheme is presented for the renormalization group calculations of physical quantities in quantum chromodynamics (QCD). Some basic formulas concerning the renormalization-scheme dependence of Green's and renormalization group functions are given. A massless asymptotically free theory with one coupling constant g is considered. In conclusion, several rules for renormalization group calculations in QCD are formulated
Renormalization group and Mayer expansions
International Nuclear Information System (INIS)
Mack, G.
1984-02-01
Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U(1) lattice gauge theory by Goepfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear sigma-model, and elsewhere. (orig.)
Renormalization group and mayer expansions
International Nuclear Information System (INIS)
Mack, G.
1984-01-01
Mayer expansions promise to become a powerful tool in exact renormalization group calculations. Iterated Mayer expansions were sucessfully used in the rigorous analysis of 3-dimensional U (1) lattice gauge theory by Gopfert and the author, and it is hoped that they will also be useful in the 2-dimensional nonlinear σ-model, and elsewhere
Renormalization group and critical phenomena
International Nuclear Information System (INIS)
Ji Qing
2004-01-01
The basic clue and the main steps of renormalization group method used for the description of critical phenomena is introduced. It is pointed out that this method really reflects the most important physical features of critical phenomena, i.e. self-similarity, and set up a practical solving method from it. This way of setting up a theory according to the features of the physical system is really a good lesson for today's physicists. (author)
Chaotic renormalization group approach to disordered systems
International Nuclear Information System (INIS)
Oliveira, P.M.C. de; Continentino, M.A.; Makler, S.S.; Anda, E.V.
1984-01-01
We study the eletronic properties of the disordered linear chain using a technique previously developed by some of the authors for an ordered chain. The equations of motion for the one electron Green function are obtained and the configuration average is done according to the GK scheme. The dynamical problem is transformed, using a renormalization group procedure, into a bidimensional map. The properties of this map are investigated and related to the localization properties of the eletronic system. (Author) [pt
Directory of Open Access Journals (Sweden)
Durães F.O.
2010-04-01
Full Text Available We apply the similarity renormalization group (SRG approach to evolve a nucleon-nucleon (N N interaction in leading-order (LO chiral eﬀective ﬁeld theory (ChEFT, renormalized within the framework of the subtracted kernel method (SKM. We derive a ﬁxed-point interaction and show the renormalization group (RG invariance in the SKM approach. We also compare the evolution of N N potentials with the subtraction scale through a SKM RG equation in the form of a non-relativistic Callan-Symanzik (NRCS equation and the evolution with the similarity cutoﬀ through the SRG transformation.
Renormalization group theory of earthquakes
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H. Saleur
1996-01-01
Full Text Available We study theoretically the physical origin of the proposed discrete scale invariance of earthquake processes, at the origin of the universal log-periodic corrections to scaling, recently discovered in regional seismic activity (Sornette and Sammis (1995. The discrete scaling symmetries which may be present at smaller scales are shown to be robust on a global scale with respect to disorder. Furthermore, a single complex exponent is sufficient in practice to capture the essential properties of the leading correction to scaling, whose real part may be renormalized by disorder, and thus be specific to the system. We then propose a new mechanism for discrete scale invariance, based on the interplay between dynamics and disorder. The existence of non-linear corrections to the renormalization group flow implies that an earthquake is not an isolated 'critical point', but is accompanied by an embedded set of 'critical points', its foreshocks and any subsequent shocks for which it may be a foreshock.
Antari, A. El; Zahir, H.; Hasnaoui, A.; Hachem, N.; Alrajhi, A.; Madani, M.; Bouziani, M. El
2018-04-01
Using the renormalization group approximation, specifically the Migdal-Kadanoff technique, we investigate the Blume-Capel model with mixed spins S = 1/2 and S = 5/2 on d-dimensional hypercubic lattice. The flow in the parameter space of the Hamiltonian and the thermodynamic functions are determined. The phase diagram of this model is plotted in the (anisotropy, temperature) plane for both cases d = 2 and d = 3 in which the system exhibits the first and second order phase transitions and critical end-points. The associated fixed points are drawn up in a table, and by linearizing the transformation at the vicinity of these points, we determine the critical exponents for d = 2 and d = 3. We have also presented a variation of the free energy derivative at the vicinity of the first and second order transitions. Finally, this work is completed by a discussion and comparison with other approximation.
Indefinite metric fields and the renormalization group
International Nuclear Information System (INIS)
Sherry, T.N.
1976-11-01
The renormalization group equations are derived for the Green functions of an indefinite metric field theory. In these equations one retains the mass dependence of the coefficient functions, since in the indefinite metric theories the masses cannot be neglected. The behavior of the effective coupling constant in the asymptotic and infrared limits is analyzed. The analysis is illustrated by means of a simple model incorporating indefinite metric fields. The model scales at first order, and at this order also the effective coupling constant has both ultra-violet and infra-red fixed points, the former being the bare coupling constant
Renormalization group flows and continual Lie algebras
International Nuclear Information System (INIS)
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by (d/dt;1), with anti-symmetric Cartan kernel K(t,t') = δ'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N vertical bar N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Baecklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Z n to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra (d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown. (author)
Products of composite operators in the exact renormalization group formalism
Pagani, C.; Sonoda, H.
2018-02-01
We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.
The Renormalization Group in Nuclear Physics
International Nuclear Information System (INIS)
Furnstahl, R.J.
2012-01-01
Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.
Renormalization Group Reduction of Non Integrable Hamiltonian Systems
International Nuclear Information System (INIS)
Tzenov, Stephan I.
2002-01-01
Based on Renormalization Group method, a reduction of non integratable multi-dimensional Hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density and for the amplitudes of the angular modes have been derived. It has been shown that these equations are precisely the Renormalization Group equations. As an application of the approach developed, the modulational diffusion in one-and-a-half degrees of freedom dynamical system has been studied in detail
The renormalization group and lattice QCD
International Nuclear Information System (INIS)
Gupta, R.
1989-01-01
This report discusses the following topics: scaling of thermodynamic quantities and critical exponents; scaling relations; block spin idea of Kadanoff; exact RG solution of the 1-d Ising model; Wilson's formulation of the renormalization group; linearized transformation matrix and classification of exponents; derivation of exponents from the eigenvalues of Τ αβ ; simple field theory: the gaussian model; linear renormalization group transformations; numerical methods: MCRG; block transformations for 4-d SU(N) LGT; asymptotic freedom makes QCD simple; non-perturbative β-function and scaling; and the holy grail: the renormalized trajectory
Renormalization group, principle of invariance and functional automodelity
International Nuclear Information System (INIS)
Shirkov, D.V.
1981-01-01
There exists a remarkable identity of functional equations describing the property of functional automodelity in diverse branches of physics: renormalization group equations in quantum field theory, functional equations of the invariance principle of the one-dimensional transport theory and some others. The origin of this identity is investigated. It is shown that the structure of these equations reflects the simple and general property of transitivity with respect to the way of fixatio of initial on effective degrees of freedom [ru
Renormalization group approach to superfluid neutron matter
Energy Technology Data Exchange (ETDEWEB)
Hebeler, K.
2007-06-06
In the present thesis superfluid many-fermion systems are investigated in the framework of the Renormalization Group (RG). Starting from an experimentally determined two-body interaction this scheme provides a microscopic approach to strongly correlated many-body systems at low temperatures. The fundamental objects under investigation are the two-point and the four-point vertex functions. We show that explicit results for simple separable interactions on BCS-level can be reproduced in the RG framework to high accuracy. Furthermore the RG approach can immediately be applied to general realistic interaction models. In particular, we show how the complexity of the many-body problem can be reduced systematically by combining different RG schemes. Apart from technical convenience the RG framework has conceptual advantage that correlations beyond the BCS level can be incorporated in the flow equations in a systematic way. In this case however the flow equations are no more explicit equations like at BCS level but instead a coupled set of implicit equations. We show on the basis of explicit calculations for the single-channel case the efficacy of an iterative approach to this system. The generalization of this strategy provides a promising strategy for a non-perturbative treatment of the coupled channel problem. By the coupling of the flow equations of the two-point and four-point vertex self-consistency on the one-body level is guaranteed at every cutoff scale. (orig.)
New renormalization group approach to multiscale problems
Energy Technology Data Exchange (ETDEWEB)
Einhorn, M B; Jones, D R.T.
1984-02-27
A new renormalization group is presented which exploits invariance with respect to more than one scale. The method is illustrated by a simple model, and future applications to fields such as critical phenomena and supersymmetry are speculated upon.
The large-Nc renormalization group
International Nuclear Information System (INIS)
Dorey, N.
1995-01-01
In this talk, we review how effective theories of mesons and baryons become exactly soluble in the large-N c , limit. We start with a generic hadron Lagrangian constrained only by certain well-known large-N c , selection rules. The bare vertices of the theory are dressed by an infinite class of UV divergent Feynman diagrams at leading order in 1/N c . We show how all these leading-order dia, grams can be summed exactly using semiclassical techniques. The saddle-point field configuration is reminiscent of the chiral bag: hedgehog pions outside a sphere of radius Λ -1 (Λ being the UV cutoff of the effective theory) matched onto nucleon degrees of freedom for r ≤ Λ -1 . The effect of this pion cloud is to renormalize the bare nucleon mass, nucleon-Δ hyperfine mass splitting, and Yukawa couplings of the theory. The corresponding large-N c , renormalization group equations for these parameters are presented, and solved explicitly in a series of simple models. We explain under what conditions the Skyrmion emerges as a UV fixed-point of the RG flow as Λ → ∞
On renormalization group flow in matrix model
International Nuclear Information System (INIS)
Gao, H.B.
1992-10-01
The renormalization group flow recently found by Brezin and Zinn-Justin by integrating out redundant entries of the (N+1)x(N+1) Hermitian random matrix is studied. By introducing explicitly the RG flow parameter, and adding suitable counter terms to the matrix potential of the one matrix model, we deduce some interesting properties of the RG trajectories. In particular, the string equation for the general massive model interpolating between the UV and IR fixed points turns out to be a consequence of RG flow. An ambiguity in the UV region of the RG trajectory is remarked to be related to the large order behaviour of the one matrix model. (author). 7 refs
Nonlinear relativistic plasma resonance: Renormalization group approach
Energy Technology Data Exchange (ETDEWEB)
Metelskii, I. I., E-mail: metelski@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation); Kovalev, V. F., E-mail: vfkvvfkv@gmail.com [Dukhov All-Russian Research Institute of Automatics (Russian Federation); Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
2017-02-15
An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined.
Large neutrino mixing from renormalization group evolution
International Nuclear Information System (INIS)
Balaji, K.R.S.; Mohapatra, R.N.; Parida, M.K.; Paschos, E.A.
2000-10-01
The renormalization group evolution equation for two neutrino mixing is known to exhibit nontrivial fixed point structure corresponding to maximal mixing at the weak scale. The presence of the fixed point provides a natural explanation of the observed maximal mixing of ν μ - ν τ , if the ν μ and ν τ are assumed to be quasi-degenerate at the seesaw scale without constraining the mixing angles at that scale. In particular, it allows them to be similar to the quark mixings as in generic grand unified theories. We discuss implementation of this program in the case of MSSM and find that the predicted mixing remains stable and close to its maximal value, for all energies below the O(TeV) SUSY scale. We also discuss how a particular realization of this idea can be tested in neutrinoless double beta decay experiments. (author)
Quantum field theory and phase transitions: universality and renormalization group
International Nuclear Information System (INIS)
Zinn-Justin, J.
2003-08-01
In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)
The applications of the renormalization group
International Nuclear Information System (INIS)
Hughes, J.L.
1988-01-01
Three applications of the exact renormalization group (RG) to field theory and string theory are developed. (1) First, β-functions are related to the flow of the relevant couplings in the exact RG. The specific case of a cutoff λφ 4 theory in four dimensions is discussed in detail. The underlying idea of convergence of the flow of effective lagrangians is developed to identify the β-functions. A perturbative calculations of the β-functions using the exact flow equations is then sketched. (2) Next, the operator product expansion (OPE) is motivated and developed within the context of effective lagrangians. The exact RG may be used to establish the asymptotic properties of the expansion. Again, the example field theory focused upon is a cutoff λφ 4 in four dimensions. A detailed proof of the asymptotics for the special case of the expansion of φ(χ)φ(0) is given. The ideas of the proof are sufficient to prove the general case of any two local operators. Although both of the above applications are developed for a cutoff λφ 4 , the analysis may be extended to any theory with a physical cutoff. (3) Finally, some consequences of the proposal by Banks and Martinec that the classical string field equation can be written as as exact RG equation are examined. Cutoff conformal field theories on the sphere are identified as possible string field configurations. The Wilson fixed-point equation is generalized to conformal invariance and then taken to be the equation of motion for the string field. The equation's solutions for a restricted set of configurations are examined - namely, closed bosonic strings in 26 dimensions. Tree-level Virasoro-Shapiro (VS) S-matrix elements emerge in what is interpreted as a weak component-field expansion of the solution
Renormalization Group and Phase Transitions in Spin, Gauge, and QCD Like Theories
Energy Technology Data Exchange (ETDEWEB)
Liu, Yuzhi [Univ. of Iowa, Iowa City, IA (United States)
2013-08-01
In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG).
Functional renormalization group approach to the two dimensional Bose gas
Energy Technology Data Exchange (ETDEWEB)
Sinner, A; Kopietz, P [Institut fuer Theoretische Physik, Universitaet Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt (Germany); Hasselmann, N [International Center for Condensed Matter Physics, Universidade de BrasIlia, Caixa Postal 04667, 70910-900 BrasIlia, DF (Brazil)], E-mail: hasselma@itp.uni-frankfurt.de, E-mail: sinner@itp.uni-frankfurt.de
2009-02-01
We investigate the small frequency and momentum structure of the weakly interacting Bose gas in two dimensions using a functional renormalization group approach. The flow equations are derived within a derivative approximation of the effective action up to second order in spatial and temporal variables and investigated numerically. The truncation we employ is based on the perturbative structure of the theory and is well described as a renormalization group enhanced perturbation theory. It allows to calculate corrections to the Bogoliubov spectrum and to investigate the damping of quasiparticles. Our approach allows to circumvent the divergences which plague the usual perturbative approach.
Renormalization group theory of critical phenomena
International Nuclear Information System (INIS)
Menon, S.V.G.
1995-01-01
Renormalization group theory is a framework for describing those phenomena that involve a multitude of scales of variations of microscopic quantities. Systems in the vicinity of continuous phase transitions have spatial correlations at all length scales. The renormalization group theory and the pertinent background material are introduced and applied to some important problems in this monograph. The monograph begins with a historical survey of thermal phase transitions. The background material leading to the renormalization group theory is covered in the first three chapters. Then, the basic techniques of the theory are introduced and applied to magnetic critical phenomena in the next four chapters. The momentum space approach as well as the real space techniques are, thus, discussed in detail. Finally, brief outlines of applications of the theory to some of the related areas are presented in the last chapter. (author)
Renormalization group and the superconducting susceptibility of a Fermi liquid
International Nuclear Information System (INIS)
Parameswaran, S. A.; Sondhi, S. L.; Shankar, R.
2010-01-01
A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does not. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.
Renormalization group approach in the turbulence theory
International Nuclear Information System (INIS)
Adzhemyan, L.Ts.; Vasil'ev, A.N.; Pis'mak, Yu.M.
1983-01-01
In the framework of the renormalization groUp approach in the turbulence theory sUggested in another paper, the problem of renormalization and evaluation of critical dimensions of composite operators is discussed. Renormalization of a system of operators of canonical dimension equal to 4, including the operator F=phiΔphi (where phi is the velocity field), is considered. It is shown that the critical dimension Δsub(F)=0. The appendice includes the brief proofs of two theorems: 1) the theorem on the equivalence between the arbitrary stochastic problem and quantum field theory; 2) the theorem which determines the reduction of Green functions of the stochastic problem to the hypersurface of coinciding times
Block generators for the similarity renormalization group
Energy Technology Data Exchange (ETDEWEB)
Huether, Thomas; Roth, Robert [TU Darmstadt (Germany)
2016-07-01
The Similarity Renormalization Group (SRG) is a powerful tool to improve convergence behavior of many-body calculations using NN and 3N interactions from chiral effective field theory. The SRG method decouples high and low-energy physics, through a continuous unitary transformation implemented via a flow equation approach. The flow is determined by a generator of choice. This generator governs the decoupling pattern and, thus, the improvement of convergence, but it also induces many-body interactions. Through the design of the generator we can optimize the balance between convergence and induced forces. We explore a new class of block generators that restrict the decoupling to the high-energy sector and leave the diagonalization in the low-energy sector to the many-body method. In this way one expects a suppression of induced forces. We analyze the induced many-body forces and the convergence behavior in light and medium-mass nuclei in No-Core Shell Model and In-Medium SRG calculations.
International Nuclear Information System (INIS)
Actis, S.; Passarino, G.
2006-12-01
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)
2006-12-15
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)
Renormalization group approach to causal bulk viscous cosmological models
International Nuclear Information System (INIS)
Belinchon, J A; Harko, T; Mak, M K
2002-01-01
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor
Renormalization group procedure for potential −g/r2
Directory of Open Access Journals (Sweden)
S.M. Dawid
2018-02-01
Full Text Available Schrödinger equation with potential −g/r2 exhibits a limit cycle, described in the literature in a broad range of contexts using various regularizations of the singularity at r=0. Instead, we use the renormalization group transformation based on Gaussian elimination, from the Hamiltonian eigenvalue problem, of high momentum modes above a finite, floating cutoff scale. The procedure identifies a richer structure than the one we found in the literature. Namely, it directly yields an equation that determines the renormalized Hamiltonians as functions of the floating cutoff: solutions to this equation exhibit, in addition to the limit-cycle, also the asymptotic-freedom, triviality, and fixed-point behaviors, the latter in vicinity of infinitely many separate pairs of fixed points in different partial waves for different values of g.
Transformation of renormalization groups in 2N-component fermion hierarchical model
International Nuclear Information System (INIS)
Stepanov, R.G.
2006-01-01
The 2N-component fermion model on the hierarchical lattice is studied. The explicit formulae for renormalization groups transformation in the space of coefficients setting the Grassmannian-significant density of the free measure are presented. The inverse transformation of the renormalization group is calculated. The definition of immovable points of renormalization groups is reduced to solving the set of algebraic equations. The interesting connection between renormalization group transformations in boson and fermion hierarchical models is found out. It is shown that one transformation is obtained from other one by the substitution of N on -N [ru
Perturbative renormalization of QED via flow equations
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1991-01-01
We prove the perturbative renormalizability of euclidean QED 4 with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.)
Perturbative renormalization of QED via flow equations
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany)); Kopper, C. (Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Munich (Germany) Inst. fuer Theoretische Physik, Univ. Goettingen (Germany))
1991-12-19
We prove the perturbative renormalizability of euclidean QED{sub 4} with a small photon mass in the framework of effective lagrangians due to Wilson and Polchinski. In particular we show that the QED identities, which become violated by our momentum space regularization at intermediate stages, are restored in the renormalized theory. (orig.).
Renormalization group flow of the Higgs potential.
Gies, Holger; Sondenheimer, René
2018-03-06
We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability.This article is part of the Theo Murphy meeting issue 'Higgs cosmology'. © 2018 The Author(s).
Renormalization group evolution of Dirac neutrino masses
International Nuclear Information System (INIS)
Lindner, Manfred; Ratz, Michael; Schmidt, Michael Andreas
2005-01-01
There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large tan β comparable to the precision of future experiments
Renormalization group in statistical physics - momentum and real spaces
International Nuclear Information System (INIS)
Yukalov, V.I.
1988-01-01
Two variants of the renormalization group approach in statistical physics are considered, the renormalization group in the momentum and the renormalization group in the real spaces. Common properties of these methods and their differences are cleared up. A simple model for investigating the crossover between different universality classes is suggested. 27 refs
Computing the effective action with the functional renormalization group
Energy Technology Data Exchange (ETDEWEB)
Codello, Alessandro [CP3-Origins and the Danish IAS University of Southern Denmark, Odense (Denmark); Percacci, Roberto [SISSA, Trieste (Italy); INFN, Sezione di Trieste, Trieste (Italy); Rachwal, Leslaw [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Tonero, Alberto [ICTP-SAIFR and IFT, Sao Paulo (Brazil)
2016-04-15
The ''exact'' or ''functional'' renormalization group equation describes the renormalization group flow of the effective average action Γ{sub k}. The ordinary effective action Γ{sub 0} can be obtained by integrating the flow equation from an ultraviolet scale k = Λ down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity. (orig.)
A renormalization group theory of cultural evolution
Fath, Gabor; Sarvary, Miklos
2003-01-01
We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequa...
The Bogolyubov renormalization group. Second English printing
International Nuclear Information System (INIS)
Shirkov, D.V.
1996-01-01
We begin with personal notes describing the atmosphere of 'Bogolyubov renormalization group' birth. Then we expose the history of RG discovery in the QFT and of the RG method devising in the mid-fifties. The third part is devoted to proliferation of RG ideas into diverse parts of theoretical physics. We conclude with discussing the perspective of RG method further development and its application in mathematical physics. 58 refs
Generalized Hubbard Hamiltonian: renormalization group approach
International Nuclear Information System (INIS)
Cannas, S.A.; Tamarit, F.A.; Tsallis, C.
1991-01-01
We study a generalized Hubbard Hamiltonian which is closed within the framework of a Quantum Real Space Renormalization Group, which replaces the d-dimensional hypercubic lattice by a diamond-like lattice. The phase diagram of the generalized Hubbard Hamiltonian is analyzed for the half-filled band case in d = 2 and d = 3. Some evidence for superconductivity is presented. (author). 44 refs., 12 figs., 2 tabs
Introduction to the nonequilibrium functional renormalization group
International Nuclear Information System (INIS)
Berges, J.; Mesterházy, D.
2012-01-01
In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.
Exact renormalization group for gauge theories
International Nuclear Information System (INIS)
Balaban, T.; Imbrie, J.; Jaffe, A.
1984-01-01
Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study
Temperature renormalization group approach to spontaneous symmetry breaking
International Nuclear Information System (INIS)
Manesis, E.; Sakakibara, S.
1985-01-01
We apply renormalization group equations that describe the finite-temperature behavior of Green's functions to investigate thermal properties of spontaneous symmetry breaking. Specifically, in the O(N).O(N) symmetric model we study the change of symmetry breaking patterns with temperature, and show that there always exists the unbroken symmetry phase at high temperature, modifying the naive result of leading order in finite-temperature perturbation theory. (orig.)
Renormalization group treatment of nonrenormalizable interactions
International Nuclear Information System (INIS)
Kazakov, D I; Vartanov, G S
2006-01-01
The structure of the UV divergences in higher dimensional nonrenormalizable theories is analysed. Based on renormalization operation and renormalization group theory it is shown that even in this case the leading divergences (asymptotics) are governed by the one-loop diagrams the number of which, however, is infinite. An explicit expression for the one-loop counter term in an arbitrary D-dimensional quantum field theory without derivatives is suggested. This allows one to sum up the leading asymptotics which are independent of the arbitrariness in subtraction of higher order operators. Diagrammatic calculations in a number of scalar models in higher loops are performed to be in agreement with the above statements. These results do not support the idea of the naive power-law running of couplings in nonrenormalizable theories and fail (with one exception) to reveal any simple closed formula for the leading terms
Can renormalization group flow end in a Big Mess?
International Nuclear Information System (INIS)
Morozov, Alexei; Niemi, Antti J.
2003-01-01
The field theoretical renormalization group equations have many common features with the equations of dynamical systems. In particular, the manner how Callan-Symanzik equation ensures the independence of a theory from its subtraction point is reminiscent of self-similarity in autonomous flows towards attractors. Motivated by such analogies we propose that besides isolated fixed points, the couplings in a renormalizable field theory may also flow towards more general, even fractal attractors. This could lead to Big Mess scenarios in applications to multiphase systems, from spin-glasses and neural networks to fundamental string (M?) theory. We consider various general aspects of such chaotic flows. We argue that they pose no obvious contradictions with the known properties of effective actions, the existence of dissipative Lyapunov functions, and even the strong version of the c-theorem. We also explain the difficulties encountered when constructing effective actions with chaotic renormalization group flows and observe that they have many common virtues with realistic field theory effective actions. We conclude that if chaotic renormalization group flows are to be excluded, conceptually novel no-go theorems must be developed
Optimization of renormalization group transformations in lattice gauge theory
International Nuclear Information System (INIS)
Lang, C.B.; Salmhofer, M.
1988-01-01
We discuss the dependence of the renormalization group flow on the choice of the renormalization group transformation (RGT). An optimal choice of the transformation's parameters should lead to a renormalized trajectory close to a few-parameter action. We apply a recently developed method to determine an optimal RGT to SU(2) lattice gauge theory and discuss the achieved improvement. (orig.)
Renormalization Group scale-setting in astrophysical systems
Domazet, Silvije; Štefančić, Hrvoje
2011-09-01
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.
Renormalization Group scale-setting in astrophysical systems
International Nuclear Information System (INIS)
Domazet, Silvije; Stefancic, Hrvoje
2011-01-01
A more general scale-setting procedure for General Relativity with Renormalization Group corrections is proposed. Theoretical aspects of the scale-setting procedure and the interpretation of the Renormalization Group running scale are discussed. The procedure is elaborated for several highly symmetric systems with matter in the form of an ideal fluid and for two models of running of the Newton coupling and the cosmological term. For a static spherically symmetric system with the matter obeying the polytropic equation of state the running scale-setting is performed analytically. The obtained result for the running scale matches the Ansatz introduced in a recent paper by Rodrigues, Letelier and Shapiro which provides an excellent explanation of rotation curves for a number of galaxies. A systematic explanation of the galaxy rotation curves using the scale-setting procedure introduced in this Letter is identified as an important future goal.
The evolution of Bogolyubov's renormalization group
International Nuclear Information System (INIS)
Shirkov, D.V.
2000-01-01
We review the evolution of the concept of Renormalization Group (RG). This notion, as was first introduced in quantum field theory (QFT) in the mid-fifties in N.N.Bogolyubov's formulation, is based upon a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of a boundary condition) specifying some particular solution. To illustrate this approach's effectiveness, we end with its application to the analysis of the laser beam self-focusing in a non-linear medium
Ultracold atoms and the Functional Renormalization Group
International Nuclear Information System (INIS)
Boettcher, Igor; Pawlowski, Jan M.; Diehl, Sebastian
2012-01-01
We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context, we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition. The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field.
Equation-free dynamic renormalization in a glassy compaction model
International Nuclear Information System (INIS)
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-01-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena
Equation-free dynamic renormalization in a glassy compaction model
Chen, L.; Kevrekidis, I. G.; Kevrekidis, P. G.
2006-07-01
Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.
International Nuclear Information System (INIS)
Maris, Th.A.J.
1976-01-01
The renormalization group theory has a natural place in a general framework of symmetries in quantum field theories. Seen in this way, a 'renormalization group' is a one-parametric subset of the direct product of dilatation and renormalization groups. This subset of spontaneously broken symmetry transformations connects the inequivalent solutions generated by a parameter-dependent regularization procedure, as occurs in renormalized perturbation theory. By considering the global, rather than the infinitesimal, transformations, an expression for general vertices is directly obtained, which is the formal solution of exact renormalization group equations [pt
Finite cluster renormalization and new two step renormalization group for Ising model
International Nuclear Information System (INIS)
Benyoussef, A.; El Kenz, A.
1989-09-01
New types of renormalization group theory using the generalized Callen identities are exploited in the study of the Ising model. Another type of two-step renormalization is proposed. Critical couplings and critical exponents y T and y H are calculated by these methods for square and simple cubic lattices, using different size clusters. (author). 17 refs, 2 tabs
Phase structure of NJL model with weak renormalization group
Aoki, Ken-Ichi; Kumamoto, Shin-Ichiro; Yamada, Masatoshi
2018-06-01
We analyze the chiral phase structure of the Nambu-Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V (σ ; t) is given as a partial differential equation, where σ : = ψ bar ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V (σ ; t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.
Renormalization group and fixed points in quantum field theory
International Nuclear Information System (INIS)
Hollowood, Timothy J.
2013-01-01
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
A renormalization group theory of cultural evolution
Fáth, Gábor; Sarvary, Miklos
2005-03-01
We present a theory of cultural evolution based upon a renormalization group scheme. We consider rational but cognitively limited agents who optimize their decision-making process by iteratively updating and refining the mental representation of their natural and social environment. These representations are built around the most important degrees of freedom of their world. Cultural coherence among agents is defined as the overlap of mental representations and is characterized using an adequate order parameter. As the importance of social interactions increases or agents become more intelligent, we observe and quantify a series of dynamic phase transitions by which cultural coherence advances in the society. A similar phase transition may explain the so-called “cultural explosion’’ in human evolution some 50,000 years ago.
Renormalization group approach to soft gluon resummation
International Nuclear Information System (INIS)
Forte, Stefano; Ridolfi, Giovanni
2003-01-01
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single dimensionful variable, and then using the renormalization group to resum them. Beyond the next-to-leading log level, our result is somewhat less predictive than previous all-order resummation formulae, but it does not rely on non-standard factorization, and it is thus possibly more general. We use our result to settle issues of convergence of the resummed series, we discuss scheme dependence at the resummed level, and we provide explicit resummed expressions in various factorization schemes
On truncations of the exact renormalization group
Morris, T R
1994-01-01
We investigate the Exact Renormalization Group (ERG) description of (Z_2 invariant) one-component scalar field theory, in the approximation in which all momentum dependence is discarded in the effective vertices. In this context we show how one can perform a systematic search for non-perturbative continuum limits without making any assumption about the form of the lagrangian. Concentrating on the non-perturbative three dimensional Wilson fixed point, we then show that the sequence of truncations n=2,3,\\dots, obtained by expanding about the field \\varphi=0 and discarding all powers \\varphi^{2n+2} and higher, yields solutions that at first converge to the answer obtained without truncation, but then cease to further converge beyond a certain point. No completely reliable method exists to reject the many spurious solutions that are also found. These properties are explained in terms of the analytic behaviour of the untruncated solutions -- which we describe in some detail.
Fermionic functional integrals and the renormalization group
Feldman, Joel; Trubowitz, Eugene
2002-01-01
This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physical intuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on the Aisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and so...
Renormalization group theory impact on experimental magnetism
Köbler, Ulrich
2010-01-01
Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are calle...
Renormalization-group analysis of the Kobayashi-Maskawa matrix
International Nuclear Information System (INIS)
Babu, K.S.
1987-01-01
The one-loop renormalization-group equations for the quark mixing (Kobayashi-Maskawa) matrix V are derived, independent of one's weak interaction basis, in the standard model as well as in its two Higgs and supersymmetric extensions, and their numerical solutions are presented. While the mixing angles vertical strokeV ub vertical stroke, vertical strokeV cb vertical stroke, vertical strokeV td vertical stroke and the phase-invariant measure of CP nonconservation J all vary slowly with momentum, in the standard model they are predicted to increase in clear contrast to the two Higgs and supersymmetric extensions where they decrease with momentum. (orig.)
Renormalization Group Theory of Bolgiano Scaling in Boussinesq Turbulence
Rubinstein, Robert
1994-01-01
Bolgiano scaling in Boussinesq turbulence is analyzed using the Yakhot-Orszag renormalization group. For this purpose, an isotropic model is introduced. Scaling exponents are calculated by forcing the temperature equation so that the temperature variance flux is constant in the inertial range. Universal amplitudes associated with the scaling laws are computed by expanding about a logarithmic theory. Connections between this formalism and the direct interaction approximation are discussed. It is suggested that the Yakhot-Orszag theory yields a lowest order approximate solution of a regularized direct interaction approximation which can be corrected by a simple iterative procedure.
Critical phenomena and renormalization group transformations
International Nuclear Information System (INIS)
Castellani, C.; Castro, C. di
1980-01-01
Our main goal is to guide the reader to find out the common rational behind the various renormalization procedures which have been proposed in the last ten years. In the first part of these lectures old arguments on universality and scaling will be briefly recalled. To our opinion these introductory remarks allow one to stress the physical origin of the two majore renormalization procedures, which have been used in the theory of critical phenomena: the Wilson and the field theoretic approach. All the general properties of a ''good'' renormalization transformation will also come out quite naturally. (author)
International Nuclear Information System (INIS)
Gulov, A.V.; Skalozub, V.V.
2000-01-01
In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop renormalization group relation is derived which gives possibility to reduce the problem to the scattering of light particles on the external field substituting a heavy virtual state. Applications of the results to problem of searching new physics beyond the Standard Model are discussed [ru
Perturbative renormalization of composite operators via flow equations. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik und Astrophysik, Muenchen (Germany). Werner-Heisenberg-Inst. fuer Physik); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1992-09-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive {Phi}{sub 4}{sup 4} theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.).
Perturbative renormalization of composite operators via flow equations. Pt. 1
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1992-01-01
We apply the general framework of the continuous renormalization group, whose significance for perturbative quantum field theories was recognized by Polchinski, to investigate by new and mathematically simple methods the perturbative renormalization of composite operators. In this paper we demonstrate the perturbative renormalizability of the Green functions of the Euclidean massive Φ 4 4 theory with one insertion of a (possibly oversubtracted, in the BPHZ language) composite operator. Moreover we show that our method admits an easy proof of the Zimmermann identities and of the Lowenstein rule. (orig.)
Nonperturbative Renormalization Group Approach to Polymerized Membranes
Essafi, Karim; Kownacki, Jean-Philippe; Mouhanna, Dominique
2014-03-01
Membranes or membrane-like materials play an important role in many fields ranging from biology to physics. These systems form a very rich domain in statistical physics. The interplay between geometry and thermal fluctuations lead to exciting phases such flat, tubular and disordered flat phases. Roughly speaking, membranes can be divided into two group: fluid membranes in which the molecules are free to diffuse and thus no shear modulus. On the other hand, in polymerized membranes the connectivity is fixed which leads to elastic forces. This difference between fluid and polymerized membranes leads to a difference in their critical behaviour. For instance, fluid membranes are always crumpled, whereas polymerized membranes exhibit a phase transition between a crumpled phase and a flat phase. In this talk, I will focus only on polymerized phantom, i.e. non-self-avoiding, membranes. The critical behaviour of both isotropic and anisotropic polymerized membranes are studied using a nonperturbative renormalization group approach (NPRG). This allows for the investigation of the phase transitions and the low temperature flat phase in any internal dimension D and embedding d. Interestingly, graphene behaves just as a polymerized membrane in its flat phase.
Functional renormalization group methods in quantum chromodynamics
International Nuclear Information System (INIS)
Braun, J.
2006-01-01
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
Renormalization-group theory of spinodal decomposition
International Nuclear Information System (INIS)
Mazenko, G.F.; Valls, O.T.; Zhang, F.C.
1985-01-01
Renormalization-group (RG) methods developed previously for the study of the growth of order in unstable systems are extended to treat the spinodal decomposition of the two-dimensional spin-exchange kinetic Ising model. The conservation of the order parameter and fixed-length sum rule are properly preserved in the theory. Various correlation functions in both coordinate and momentum space are calculated as functions of time. The scaling function for the structure factor is extracted. We compare our results with direct Monte Carlo (MC) simulations and find them in good agreement. The time rescaling parameter entering the RG analysis is temperature dependent, as was determined in previous work through a RG analysis of MC simulations. The results exhibit a long-time logarithmic growth law for the typical domain size, both analytically and numerically. In the time region where MC simulations have previously been performed, the logarithmic growth law can be fitted to a power law with an effective exponent. This exponent is found to be in excellent agreement with the result of MC simulations. The logarithmic growth law agrees with a physical model of interfacial motion which involves an interplay between the local curvature and an activated jump across the interface
Functional renormalization group methods in quantum chromodynamics
Energy Technology Data Exchange (ETDEWEB)
Braun, J.
2006-12-18
We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)
Renormalization group treatment for spin waves in the randomly disordered Heisenberg chain
International Nuclear Information System (INIS)
Chaves, C.M.; Koiller, B.
1983-03-01
Local densities of states in the randomly disordered binary quantum Heisenberg chain using a generalization of a recently developed approach based on renormalization group ideas are calculated. It envolves decimating alternate apins along the chain in such a way as to obtain recursion relations to describe the renormalized set of Green's function equations of motion. The densities of states are richly structured, indicating that the method takes into account compositional fluctuations of arbitrary range. (Author) [pt
Renormalization-group theory for the eddy viscosity in subgrid modeling
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
Effective field renormalization group approach for Ising lattice spin systems
Fittipaldi, Ivon P.
1994-03-01
A new applicable real-space renormalization group framework (EFRG) for computing the critical properties of Ising lattice spin systems is presented. The method, which follows up the same strategy of the mean-field renormalization group scheme (MFRG), is based on rigorous Ising spin identities and utilizes a convenient differential operator expansion technique. Within this scheme, in contrast with the usual mean-field type of equation of state, all the relevant self-spin correlations are taken exactly into account. The results for the critical coupling and the critical exponent v, for the correlation length, are very satisfactory and it is shown that this technique leads to rather accurate results which represent a remarkable improvement on those obtained from the standard MFRG method. In particular, it is shown that the present EFRG approach correctly distinguishes the geometry of the lattice structure even when employing its simplest size-cluster version. Owing to its simplicity we also comment on the wide applicability of the present method to problems in crystalline and disordered Ising spin systems.
Renormalization group theory of phase transitions in square Ising systems
International Nuclear Information System (INIS)
Nienhuis, B.
1978-01-01
Some renormalization group calculations are presented on a number of phase transitions in a square Ising model, both second and first order. Of these transitions critical exponents are calculated, the amplitudes of the power law divergences and the locus of the transition. In some cases attention is paid to the thermodynamic functions also far from the critical point. Universality and scaling are discussed and the renormalization group theory is reviewed. It is shown how a renormalization transformation, which relates two similar systems with different macroscopic dimensions, can be constructed, and how some critical properties of the system follow from this transformation. Several numerical and analytical applications are presented. (Auth.)
Exact renormalization group as a scheme for calculations
International Nuclear Information System (INIS)
Mack, G.
1985-10-01
In this lecture I report on recent work to use exact renormalization group methods to construct a scheme for calculations in quantum field theory and classical statistical mechanics on the continuum. (orig./HSI)
Dynamical renormalization group approach to relaxation in quantum field theory
International Nuclear Information System (INIS)
Boyanovsky, D.; Vega, H.J. de
2003-01-01
The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths
The renormalization group: scale transformations and changes of scheme
International Nuclear Information System (INIS)
Roditi, I.
1983-01-01
Starting from a study of perturbation theory, the renormalization group is expressed, not only for changes of scale but also within the original view of Stueckelberg and Peterman, for changes of renormalization scheme. The consequences that follow from using that group are investigated. Following a more general point of view a method to obtain an improvement of the perturbative results for physical quantities is proposed. The results obtained with this method are compared with those of other existing methods. (L.C.) [pt
Probing renormalization group flows using entanglement entropy
International Nuclear Information System (INIS)
Liu, Hong; Mezei, Márk
2014-01-01
In this paper we continue the study of renormalized entanglement entropy introduced in http://dx.doi.org/10.1007/JHEP04(2013)162. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen
Fermi-edge singularity and the functional renormalization group
Kugler, Fabian B.; von Delft, Jan
2018-05-01
We study the Fermi-edge singularity, describing the response of a degenerate electron system to optical excitation, in the framework of the functional renormalization group (fRG). Results for the (interband) particle-hole susceptibility from various implementations of fRG (one- and two-particle-irreducible, multi-channel Hubbard–Stratonovich, flowing susceptibility) are compared to the summation of all leading logarithmic (log) diagrams, achieved by a (first-order) solution of the parquet equations. For the (zero-dimensional) special case of the x-ray-edge singularity, we show that the leading log formula can be analytically reproduced in a consistent way from a truncated, one-loop fRG flow. However, reviewing the underlying diagrammatic structure, we show that this derivation relies on fortuitous partial cancellations special to the form of and accuracy applied to the x-ray-edge singularity and does not generalize.
Functional renormalization group study of fluctuation effects in fermionic superfluids
Energy Technology Data Exchange (ETDEWEB)
Eberlein, Andreas
2013-03-22
This thesis is concerned with ground state properties of two-dimensional fermionic superfluids. In such systems, fluctuation effects are particularly strong and lead for example to a renormalization of the order parameter and to infrared singularities. In the first part of this thesis, the fermionic two-particle vertex is analysed and the fermionic renormalization group is used to derive flow equations for a decomposition of the vertex in charge, magnetic and pairing channels. In the second part, the channel-decomposition scheme is applied to various model systems. In the superfluid state, the fermionic two-particle vertex develops rich and singular dependences on momentum and frequency. After simplifying its structure by exploiting symmetries, a parametrization of the vertex in terms of boson-exchange interactions in the particle-hole and particle-particle channels is formulated, which provides an efficient description of the singular momentum and frequency dependences. Based on this decomposition of the vertex, flow equations for the effective interactions are derived on one- and two-loop level, extending existing channel-decomposition schemes to (i) the description of symmetry breaking in the Cooper channel and (ii) the inclusion of those two-loop renormalization contributions to the vertex that are neglected in the Katanin scheme. In the second part, the superfluid ground state of various model systems is studied using the channel-decomposition scheme for the vertex and the flow equations. A reduced model with interactions in the pairing and forward scattering channels is solved exactly, yielding insights into the singularity structure of the vertex. For the attractive Hubbard model at weak coupling, the momentum and frequency dependence of the two-particle vertex and the frequency dependence of the self-energy are determined on one- and two-loop level. Results for the suppression of the superfluid gap by fluctuations are in good agreement with the literature
Anisotropic square lattice Potts ferromagnet: renormalization group treatment
International Nuclear Information System (INIS)
Oliveira, P.M.C. de; Tsallis, C.
1981-01-01
The choice of a convenient self-dual cell within a real space renormalization group framework enables a satisfactory treatment of the anisotropic square lattice q-state Potts ferromagnet criticality. The exact critical frontier and dimensionality crossover exponent PHI as well as the expected universality behaviour (renormalization flow sense) are recovered for any linear scaling factor b and all values of q(q - [pt
Renormalization group analysis of a simple hierarchical fermion model
International Nuclear Information System (INIS)
Dorlas, T.C.
1991-01-01
A simple hierarchical fermion model is constructed which gives rise to an exact renormalization transformation in a 2-dimensional parameter space. The behaviour of this transformation is studied. It has two hyperbolic fixed points for which the existence of a global critical line is proven. The asymptotic behaviour of the transformation is used to prove the existence of the thermodynamic limit in a certain domain in parameter space. Also the existence of a continuum limit for these theories is investigated using information about the asymptotic renormalization behaviour. It turns out that the 'trivial' fixed point gives rise to a two-parameter family of continuum limits corresponding to that part of parameter space where the renormalization trajectories originate at this fixed point. Although the model is not very realistic it serves as a simple example of the appliclation of the renormalization group to proving the existence of the thermodynamic limit and the continuum limit of lattice models. Moreover, it illustrates possible complications that can arise in global renormalization group behaviour, and that might also be present in other models where no global analysis of the renormalization transformation has yet been achieved. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Daum, Jan-Eric
2011-03-11
Whereas the Standard Model of elementary particle physics represents a consistent, renormalizable quantum field theory of three of the four known interactions, the quantization of gravity still remains an unsolved problem. However, in recent years evidence for the asymptotic safety of gravity was provided. That means that also for gravity a quantum field theory can be constructed that is renormalizable in a generalized way which does not explicitly refer to perturbation theory. In addition, this approach, that is based on the Wilsonian renormalization group, predicts the correct microscopic action of the theory. In the classical framework, metric gravity is equivalent to the Einstein-Cartan theory on the level of the vacuum field equations. The latter uses the tetrad e and the spin connection {omega} as fundamental variables. However, this theory possesses more degrees of freedom, a larger gauge group, and its associated action is of first order. All these features make a treatment analogue to metric gravity much more difficult. In this thesis a three-dimensional truncation of the form of a generalized Hilbert-Palatini action is analyzed. Besides the running of Newton's constant G{sub k} and the cosmological constant {lambda}{sub k}, it also captures the renormalization of the Immirzi parameter {gamma}{sub k}. In spite of the mentioned difficulties, the spectrum of the free Hilbert-Palatini propagator can be computed analytically. On its basis, a proper time-like flow equation is constructed. Furthermore, appropriate gauge conditions are chosen and analyzed in detail. This demands a covariantization of the gauge transformations. The resulting flow is analyzed for different regularization schemes and gauge parameters. The results provide convincing evidence for asymptotic safety within the (e,{omega}) approach as well and therefore for the possible existence of a mathematically consistent and predictive fundamental quantum theory of gravity. In particular, one
The renormalization group in effective chiral theories
International Nuclear Information System (INIS)
Varin, T.
2007-09-01
The dilepton production within the heavy ions collisions (CERN/SPS, SIS/HADES, RHIC) and the behaviour of vector mesons (in particular the rho meson) are among the main topics of quantum chromodynamics (QCD) in hadronic matter. One of the main goals is the study of partial or total restoration of chiral symmetry SU(2) x SU(2), for which effective theories need to be used. One of the important difficulties is to build a theory which allows to obtain predictions when approaching the phase transition by taking into account the phenomenological constraints at low temperature and/or density. The model used here (developed by M. Urban) is based on the gauged (rho and al mesons) linear sigma model adjusted (in practice the local symmetry is only approximate) to reproduce the phenomenology very well. The first part of this thesis consists in presenting a new cut-off based regularization scheme preserving symmetry requirements. The motivation of such a method is a correct accounting of quadratic and logarithmic divergences in view of their intensive use for the renormalisation group equations. For illustrative purposes we have applied it to QED in 4 and 5 dimensions. The second part of this work is devoted to the derivation of the RGE and their resolution. In particular, we show that both restorations (traditional and vector manifestation) can be obtained from our equations, but the most likely remains the 'traditional' Ginzburg-Landau scenario. (author)
Renormalization Group in different fields of theoretical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1992-02-01
A very simple and general approach to the symmetry that is widely known as a Renormalization Group symmetry is presented. It essentially uses a functional formulation of group transformations that can be considered as a generalization of self-similarity transformations well known in mathematical physics since last century. This generalized Functional Self-Similarity symmetry and corresponding group transformations are discussed first for a number of simple physical problems taken from diverse fields of classical physics as well as for QED. Then we formulate the Renorm-Group Method as a regular procedure that essentially improves the approximate solutions near the singularity. After that we discuss relations between different formulations of Renormalization Group as they appear in various parts of a modern theoretical physics. Finally we present several topics of RGM application in modern QFT. (author)
Renormalization group analysis of the temperature dependent coupling constant in massless theory
International Nuclear Information System (INIS)
Yamada, Hirofumi.
1987-06-01
A general analysis of finite temperature renormalization group equations for massless theories is presented. It is found that in a direction where momenta and temperature are scaled up with their ratio fixed the coupling constant behaves in the same manner as in zero temperature and that asymptotic freedom at short distances is also maintained at finite temperature. (author)
The ab-initio density matrix renormalization group in practice.
Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
The ab-initio density matrix renormalization group in practice
Energy Technology Data Exchange (ETDEWEB)
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Wetting transitions: A functional renormalization-group approach
International Nuclear Information System (INIS)
Fisher, D.S.; Huse, D.A.
1985-01-01
A linear functional renormalization group is introduced as a framework in which to treat various wetting transitions of films on substrates. A unified treatment of the wetting transition in three dimensions with short-range interactions is given. The results of Brezin, Halperin, and Leibler in their three different regimes are reproduced along with new results on the multicritical behavior connecting the various regimes. In addition, the critical behavior as the coexistence curve is approached at complete wetting is analyzed. Wetting in the presence of long-range substrate-film interactions that fall off as power laws is also studied. The possible effects of the nonlinear terms in the renormalization group are examined briefly and it appears that they do not alter the critical behavior found using the truncated linear renormalization group
Fermionic renormalization group methods for transport through inhomogeneous Luttinger liquids
International Nuclear Information System (INIS)
Meden, V; Schoeller, H; Andergassen, S; Enss, T; Schoenhammer, K
2008-01-01
We compare two fermionic renormalization group (RG) methods which have been used to investigate the electronic transport properties of one-dimensional metals with two-particle interaction (Luttinger liquids) and local inhomogeneities. The first one is a poor man's method set-up to resum 'leading-log' divergences of the effective transmission at the Fermi momentum. Generically the resulting equations can be solved analytically. The second approach is based on the functional RG (fRG) method and leads to a set of differential equations which can only for certain set-ups and in limiting cases be solved analytically, while in general it must be integrated numerically. Both methods are claimed to be applicable for inhomogeneities of arbitrary strength and to capture effects of the two-particle interaction, such as interaction dependent exponents, up to leading order. We critically review this for the simplest case of a single impurity. While on first glance the poor man's approach seems to describe the crossover from the 'perfect' to the 'open chain fixed point' we collect evidence that difficulties may arise close to the 'perfect chain fixed point'. Due to a subtle relation between the scaling dimensions of the two fixed points this becomes apparent only in a detailed analysis. In the fRG method the coupling of the different scattering channels is kept which leads to a better description of the underlying physics
Fine-grained entanglement loss along renormalization-group flows
International Nuclear Information System (INIS)
Latorre, J.I.; Rico, E.; Luetken, C.A.; Vidal, G.
2005-01-01
We explore entanglement loss along renormalization group trajectories as a basic quantum information property underlying their irreversibility. This analysis is carried out for the quantum Ising chain as a transverse magnetic field is changed. We consider the ground-state entanglement between a large block of spins and the rest of the chain. Entanglement loss is seen to follow from a rigid reordering, satisfying the majorization relation, of the eigenvalues of the reduced density matrix for the spin block. More generally, our results indicate that it may be possible to prove the irreversibility along renormalization group trajectories from the properties of the vacuum only, without need to study the whole Hamiltonian
Effective-field renormalization-group method for Ising systems
Fittipaldi, I. P.; De Albuquerque, D. F.
1992-02-01
A new applicable effective-field renormalization-group (ERFG) scheme for computing critical properties of Ising spins systems is proposed and used to study the phase diagrams of a quenched bond-mixed spin Ising model on square and Kagomé lattices. The present EFRG approach yields results which improves substantially on those obtained from standard mean-field renormalization-group (MFRG) method. In particular, it is shown that the EFRG scheme correctly distinguishes the geometry of the lattice structure even when working with the smallest possible clusters, namely N'=1 and N=2.
The quantum-field renormalization group in the problem of a growing phase boundary
International Nuclear Information System (INIS)
Antonov, N.V.; Vasil'ev, A.N.
1995-01-01
Within the quantum-field renormalization-group approach we examine the stochastic equation discussed by S.I. Pavlik in describing a randomly growing phase boundary. We show that, in contrast to Pavlik's assertion, the model is not multiplicatively renormalizable and that its consistent renormalization-group analysis requires introducing an infinite number of counterterms and the respective coupling constants (open-quotes chargeclose quotes). An explicit calculation in the one-loop approximation shows that a two-dimensional surface of renormalization-group points exits in the infinite-dimensional charge space. If the surface contains an infrared stability region, the problem allows for scaling with the nonuniversal critical dimensionalities of the height of the phase boundary and time, δ h and δ t , which satisfy the exact relationship 2 δ h = δ t + d, where d is the dimensionality of the phase boundary. 23 refs., 1 tab
Distribution of the minimum path on percolation clusters: A renormalization group calculation
International Nuclear Information System (INIS)
Hipsh, Lior.
1993-06-01
This thesis uses the renormalization group for the research of the chemical distance or the minimal path on percolation clusters on a 2 dimensional square lattice. Our aims are to calculate analytically (iterative calculation) the fractal dimension of the minimal path. d min. , and the distributions of the minimum paths, l min for different lattice sizes and for different starting densities (including the threshold value p c ). For the distributions. We seek for an analytic form which describes them. The probability to get a minimum path for each linear size L is calculated by iterating the distribution of l min for the basic cell of size 2*2 to the next scale sizes, using the H cell renormalization group. For the threshold value of p and for values near to p c . We confirm a scaling in the form: P(l,L) =f1/l(l/(L d min ). L - the linear size, l - the minimum path. The distribution can be also represented in the Fourier space, so we will try to solve the renormalization group equations in this space. A numerical fitting is produced and compared to existing numerical results. In order to improve the agreement between the renormalization group and the numerical simulations, we also present attempts to generalize the renormalization group by adding more parameters, e.g. correlations between bonds in different directions or finite densities for occupation of bonds and sites. (author) 17 refs
Bogolyubov renormalization group and symmetry of solution in mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.; Kovalev, V.F.
2000-01-01
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium
Renormalization group study of scalar field theories
International Nuclear Information System (INIS)
Hasenfratz, A.; Hasenfratz, P.
1986-01-01
An approximate RG equation is derived and studied in scalar quantum field theories in d dimensions. The approximation allows for an infinite number of different couplings in the potential, but excludes interactions containing derivatives. The resulting non-linear partial differential equation can be studied by simple means. Both the gaussian and the non-gaussian fixed points are described qualitatively correctly by the equation. The RG flows in d=4 and the problem of defining an ''effective'' field theory are discussed in detail. (orig.)
Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking
Energy Technology Data Exchange (ETDEWEB)
Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi [Kanazawa Univ., Inst. for Theoretical Physics, Kanazawa, Ishikawa (Japan)
2000-04-01
The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)
Non-ladder extended renormalization group analysis of the dynamical chiral symmetry breaking
International Nuclear Information System (INIS)
Aoki, Ken-Ichi; Takagi, Kaoru; Terao, Haruhiko; Tomoyose, Masashi
2000-01-01
The order parameters of dynamical chiral symmetry breaking in QCD, the dynamical mass of quarks and the chiral condensates, are evaluated by numerically solving the non-perturbative renormalization group (NPRG) equations. We employ an approximation scheme beyond 'the ladder', that is, beyond the (improved) ladder Schwinger-Dyson equations. The chiral condensates are enhanced in comparison with the ladder approximation, which is phenomenologically favorable. The gauge dependence of the order parameters is reduced significantly in this scheme. (author)
Low-temperature approach to the renormalization-group study of critical phenomena
International Nuclear Information System (INIS)
Suranyi, P.
1977-01-01
A new method of exploring the contents of the renormalization-group equations for discrete spins is introduced. The equations are expanded in low-temperature series and the truncated series are used to obtain the critical exponents and critical temperature of a system. The method is demonstrated on the planar triangular Ising lattice and the critical parameters are found to be within a few percent of the exactly known values in third nonvanishing order of approximation
Quantum renormalization group approach to geometric phases in spin chains
International Nuclear Information System (INIS)
Jafari, R.
2013-01-01
A relation between geometric phases and criticality of spin chains are studied using the quantum renormalization-group approach. I have shown how the geometric phase evolve as the size of the system becomes large, i.e., the finite size scaling is obtained. The renormalization scheme demonstrates how the first derivative of the geometric phase with respect to the field strength diverges at the critical point and maximum value of the first derivative, and its position, scales with the exponent of the system size
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
Energy Technology Data Exchange (ETDEWEB)
Groh, Kai
2012-10-15
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement
Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies
International Nuclear Information System (INIS)
Groh, Kai
2012-10-01
The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of
On Newton-Cartan local renormalization group and anomalies
Energy Technology Data Exchange (ETDEWEB)
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); INFN Sezione di Perugia,Via A. Pascoli, 06123 Perugia (Italy); Baiguera, Stefano; Filippini, Francesco [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore,Via Musei 41, 25121 Brescia (Italy); TIFPA - INFN, c/o Dipartimento di Fisica, Università di Trento,38123 Povo (Italy)
2016-11-28
Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.
Renormalization group coupling flow of SU(3) gauge theory
QCDTARO Collaboration
1998-01-01
We present our new results on the renormalization group coupling flow obtained i n 3 dimensional coupling space $(\\beta_{11},\\beta_{12},\\beta_{twist})$. The value of $\\beta_{twist}$ turns out to be small and the coupling flow projected on $(\\beta_{11},\\beta_{12})$ plane is very similar with the previous result obtained in the 2 dimensional coupling space.
Finite cluster renormalization group for disordered two-dimensional systems
International Nuclear Information System (INIS)
El Kenz, A.
1987-09-01
A new type of renormalization group theory using the generalized Callen identities is exploited in the study of the disordered systems. Bond diluted and frustrated Ising systems on a square lattice are analyzed with this new scheme. (author). 9 refs, 2 figs, 2 tabs
Renormalization group decimation technique for disordered binary harmonic chains
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-10-01
The density of states of disordered binary harmonic chains is calculated using the Renormalization Group Decimation technique on the displacements of the masses from their equilibrium positions. The results are compared with numerical simulation data and with those obtained with the current method of Goncalves da Silva and Koiller. The advantage of our procedure over other methods is discussed. (author)
Renormalization group invariance in the presence of an instanton
International Nuclear Information System (INIS)
Ross, D.A.
1987-01-01
A pure Yang-Mills theory which admits an instanton is under discussion. n=1 supersymmetric (SU-2) Yang-Mills theory, both in the Wess-zumino gauge and in manifestly supersymmetric supergauge is considered. Two-loop vacuum graphs are calculated. The way a renormalization group invariance works under conditions of fermionic zero mode elimination is shown
On Newton-Cartan local renormalization group and anomalies
International Nuclear Information System (INIS)
Auzzi, Roberto; Baiguera, Stefano; Filippini, Francesco; Nardelli, Giuseppe
2016-01-01
Weyl consistency conditions are a powerful tool to study the irreversibility properties of the renormalization group. We apply this formalism to non-relativistic theories in 2 spatial dimensions with boost invariance and dynamical exponent z=2. Different possibilities are explored, depending on the structure of the gravitational background used as a source for the energy-momentum tensor.
Real-space renormalization group approach to driven diffusive systems
Energy Technology Data Exchange (ETDEWEB)
Hanney, T [SUPA and School of Physics, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ (United Kingdom); Stinchcombe, R B [Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP (United Kingdom)
2006-11-24
We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase.
Real-space renormalization group approach to driven diffusive systems
International Nuclear Information System (INIS)
Hanney, T; Stinchcombe, R B
2006-01-01
We introduce a real-space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties. We apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram, as well as the crossovers in the relaxation dynamics for each phase
Migdal-Kadanoff renormalization group for the Z(5) model
International Nuclear Information System (INIS)
Baltar, V.L.V.; Carneiro, G.M.; Pol, M.E.; Zagury, N.
1984-01-01
The Migdal-Kadanoff renormalization group methods is used to calculate the phase diagram of the AF Z(5) model. It is found that this scheme simulates a fixed line which it is interpreted as the locus of attraction of a critical phase. This result is in reasonable agreement with the predictions of Monte Carlo simulations. (Author) [pt
International Nuclear Information System (INIS)
Boyanovsky, Daniel; Vega, Hector J. de; Wang Shangyung
2003-01-01
The dc electrical conductivity of an ultrarelativistic QED plasma is studied in real time by implementing the dynamical renormalization group. The conductivity is obtained from the real-time dependence of a dissipative kernel closely related to the retarded photon polarization. Pinch singularities in the imaginary part of the polarization are manifest as secular terms that grow in time in the perturbative expansion of this kernel. The leading secular terms are studied explicitly and it is shown that they are insensitive to the anomalous damping of hard fermions as a result of a cancellation between self-energy and vertex corrections. The resummation of the secular terms via the dynamical renormalization group leads directly to a renormalization group equation in real time, which is the Boltzmann equation for the (gauge invariant) fermion distribution function. A direct correspondence between the perturbative expansion and the linearized Boltzmann equation is established, allowing a direct identification of the self-energy and vertex contributions to the collision term. We obtain a Fokker-Planck equation in momentum space that describes the dynamics of the departure from equilibrium to leading logarithmic order in the coupling. This equation determines that the transport time scale is given by t tr =24 π/e 4 T ln(1/e). The solution of the Fokker-Planck equation approaches asymptotically the steady-state solution as ∼e -t/(4.038...t tr ) . The steady-state solution leads to the conductivity σ=15.698 T/e 2 ln(1/e) to leading logarithmic order. We discuss the contributions beyond leading logarithms as well as beyond the Boltzmann equation. The dynamical renormalization group provides a link between linear response in quantum field theory and kinetic theory
Anatomy of the magnetic catalysis by renormalization-group method
Hattori, Koichi; Itakura, Kazunori; Ozaki, Sho
2017-12-01
We first examine the scaling argument for a renormalization-group (RG) analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and Schwinger-Dyson equations, we discuss an equivalence between these two approaches. Focusing on QED and Nambu-Jona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.
Spectral functions and transport coefficients from the functional renormalization group
Energy Technology Data Exchange (ETDEWEB)
Tripolt, Ralf-Arno
2015-06-03
In this thesis we present a new method to obtain real-time quantities like spectral functions and transport coefficients at finite temperature and density using the Functional Renormalization Group approach. Our non-perturbative method is thermodynamically consistent, symmetry preserving and based on an analytic continuation from imaginary to real time on the level of the flow equations. We demonstrate the applicability of this method by calculating mesonic spectral functions as well as the shear viscosity for the quark-meson model. In particular, results are presented for the pion and sigma spectral function at finite temperature and chemical potential, with a focus on the regime near the critical endpoint in the phase diagram of the quark-meson model. Moreover, the different time-like and space-like processes, which give rise to a complex structure of the spectral functions, are discussed. Finally, based on the momentum dependence of the spectral functions, we calculate the shear viscosity and the shear viscosity to entropy density ratio using the corresponding Green-Kubo formula.
Anatomy of the magnetic catalysis by renormalization-group method
Directory of Open Access Journals (Sweden)
Koichi Hattori
2017-12-01
Full Text Available We first examine the scaling argument for a renormalization-group (RG analysis applied to a system subject to the dimensional reduction in strong magnetic fields, and discuss the fact that a four-Fermi operator of the low-energy excitations is marginal irrespective of the strength of the coupling constant in underlying theories. We then construct a scale-dependent effective four-Fermi interaction as a result of screened photon exchanges at weak coupling, and establish the RG method appropriately including the screening effect, in which the RG evolution from ultraviolet to infrared scales is separated into two stages by the screening-mass scale. Based on a precise agreement between the dynamical mass gaps obtained from the solutions of the RG and SchwingerâDyson equations, we discuss an equivalence between these two approaches. Focusing on QED and NambuâJona-Lasinio model, we clarify how the properties of the interactions manifest themselves in the mass gap, and point out an importance of respecting the intrinsic energy-scale dependences in underlying theories for the determination of the mass gap. These studies are expected to be useful for a diagnosis of the magnetic catalysis in QCD.
Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review
Wu, Xing-Gang; Ma, Yang; Wang, Sheng-Quan; Fu, Hai-Bing; Ma, Hong-Hao; Brodsky, Stanley J.; Mojaza, Matin
2015-12-01
A valid prediction for a physical observable from quantum field theory should be independent of the choice of renormalization scheme—this is the primary requirement of renormalization group invariance (RGI). Satisfying scheme invariance is a challenging problem for perturbative QCD (pQCD), since a truncated perturbation series does not automatically satisfy the requirements of the renormalization group. In a previous review, we provided a general introduction to the various scale setting approaches suggested in the literature. As a step forward, in the present review, we present a discussion in depth of two well-established scale-setting methods based on RGI. One is the ‘principle of maximum conformality’ (PMC) in which the terms associated with the β-function are absorbed into the scale of the running coupling at each perturbative order; its predictions are scheme and scale independent at every finite order. The other approach is the ‘principle of minimum sensitivity’ (PMS), which is based on local RGI; the PMS approach determines the optimal renormalization scale by requiring the slope of the approximant of an observable to vanish. In this paper, we present a detailed comparison of the PMC and PMS procedures by analyzing two physical observables R e+e- and Γ(H\\to b\\bar{b}) up to four-loop order in pQCD. At the four-loop level, the PMC and PMS predictions for both observables agree within small errors with those of conventional scale setting assuming a physically-motivated scale, and each prediction shows small scale dependences. However, the convergence of the pQCD series at high orders, behaves quite differently: the PMC displays the best pQCD convergence since it eliminates divergent renormalon terms; in contrast, the convergence of the PMS prediction is questionable, often even worse than the conventional prediction based on an arbitrary guess for the renormalization scale. PMC predictions also have the property that any residual dependence on
Renormalization-group study of the four-body problem
International Nuclear Information System (INIS)
Schmidt, Richard; Moroz, Sergej
2010-01-01
We perform a renormalization-group analysis of the nonrelativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the region where the scattering length is infinite and all energies are close to the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of others that the four-body problem is universal, now also from a renormalization-group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound-state spectrum and comment on the influence of effective range corrections.
Scaling algebras and renormalization group in algebraic quantum field theory
International Nuclear Information System (INIS)
Buchholz, D.; Verch, R.
1995-01-01
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary spacetime manifolds and provides a framework for the systematic analysis of the short distance properties of local quantum field theories. It is shown that every theory has a (possibly non-unique) scaling limit which can be classified according to its classical or quantum nature. Dilation invariant theories are stable under the action of the renormalization group. Within this framework the problem of wedge (Bisognano-Wichmann) duality in the scaling limit is discussed and some of its physical implications are outlined. (orig.)
The density-matrix renormalization group: a short introduction.
Schollwöck, Ulrich
2011-07-13
The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.
Evaluation of spectral zeta-functions with the renormalization group
International Nuclear Information System (INIS)
Boettcher, Stefan; Li, Shanshan
2017-01-01
We evaluate spectral zeta-functions of certain network Laplacians that can be treated exactly with the renormalization group. As specific examples we consider a class of Hanoi networks and those hierarchical networks obtained by the Migdal–Kadanoff bond moving scheme from regular lattices. As possible applications of these results we mention quantum search algorithms as well as synchronization, which we discuss in more detail. (paper)
Disordered systems and the functional renormalization group, a pedagogical introduction
International Nuclear Information System (INIS)
Wiese, K.J.
2002-01-01
In this article, we review basic facts about disordered systems, especially the existence of many metastable states and and the resulting failure of dimensional reduction. Besides techniques based on the Gaussian variational method and replica-symmetry breaking (RSB), the functional renormalization group (FRG) is the only general method capable of attacking strongly disordered systems. We explain the basic ideas of the latter method and why it is difficult to implement. We finally review current progress for elastic manifolds in disorder (Author)
Nonthermal fixed points and the functional renormalization group
International Nuclear Information System (INIS)
Berges, Juergen; Hoffmeister, Gabriele
2009-01-01
Nonthermal fixed points represent basic properties of quantum field theories, in addition to vacuum or thermal equilibrium fixed points. The functional renormalization group on a closed real-time path provides a common framework for their description. For the example of an O(N) symmetric scalar theory it reveals a hierarchy of fixed point solutions, with increasing complexity from vacuum and thermal equilibrium to nonequilibrium
The Bogolyubov renormalization group in theoretical and mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1999-01-01
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part I) partially overlaps with corresponding text of my previous commemorative paper - see Ref. [6] in the list. At the same time the second part includes some fresh results in QFT (Sect. 2.1.) and summarizes (Sect. 2.4) an impressive recent progress of the 'QFT renormalization group' application in mathematical physics
Renormalization-group flows and charge transmutation in string theory
International Nuclear Information System (INIS)
Orlando, D.; Petropoulos, P.M.; Sfetsos, K.
2006-01-01
We analyze the behaviour of heterotic squashed-Wess-Zumino-Witten backgrounds under renormalization-group flow. The flows we consider are driven by perturbation creating extra gauge fluxes. We show how the conformal point acts as an attractor from both the target-space and world-sheet points of view. We also address the question of instabilities created by the presence of closed time-like curves in string backgrounds. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Real space renormalization group for spectra and density of states
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1984-09-01
We discuss the implementation of the Real Space Renormalization Group Decimation Technique for 1-d tight-binding models with long range interactions with or without disorder and for the 2-d regular square lattice. The procedure follows the ideas developed by Southern et al. Some new explicit formulae are included. The purpose of this study is to calculate spectra and densities of states following the procedure developed in our previous work. (author)
Renormalization group fixed points of foliated gravity-matter systems
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Biemans, Jorn [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Platania, Alessia [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands); Department of Physics and Astronomy, University of Catania,Via S. Sofia 63, 95123 Catania (Italy); INFN, Catania section,Via S. Sofia 64, 95123, Catania (Italy); INAF, Catania Astrophysical Observatory,Via S. Sofia 78, 95123, Catania (Italy); Saueressig, Frank [Institute for Mathematics, Astrophysics and Particle Physics (IMAPP),Radboud University Nijmegen,Heyendaalseweg 135, 6525 AJ Nijmegen (Netherlands)
2017-05-17
We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields. The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) “time”-direction. In this work, we provide a detailed derivation of the renormalization group flow of Newton’s constant and the cosmological constant on a flat Friedmann-Robertson-Walker background. Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters d{sub g}, d{sub λ}. We classify the resulting fixed point structure as a function of these parameters finding that the existence of non-Gaussian renormalization group fixed points is rather generic. In particular the matter content of the standard model and its most common extensions gives rise to one non-Gaussian fixed point with real critical exponents suitable for Asymptotic Safety. Moreover, we find non-Gaussian fixed points for any number of scalar matter fields, making the scenario attractive for cosmological model building.
Renormalization group approach to Sudakov resummation in prompt photon production
International Nuclear Information System (INIS)
Bolzoni, Paolo; Forte, Stefano; Ridolfi, Giovanni
2005-01-01
We prove the all-order exponentiation of soft logarithmic corrections to prompt photon production in hadronic collisions, by generalizing an approach previously developed in the context of Drell-Yan production and deep-inelastic scattering. We show that all large logs in the soft limit can be expressed in terms of two dimensionful variables, and we use the renormalization group to resum them. The resummed results that we obtain are more general though less predictive than those proposed by other groups, in that they can accommodate for violations of Sudakov factorization
Functional renormalization group approach to interacting three-dimensional Weyl semimetals
Sharma, Anand; Scammell, Arthur; Krieg, Jan; Kopietz, Peter
2018-03-01
We investigate the effect of long-range Coulomb interaction on the quasiparticle properties and the dielectric function of clean three-dimensional Weyl semimetals at zero temperature using a functional renormalization group (FRG) approach. The Coulomb interaction is represented via a bosonic Hubbard-Stratonovich field which couples to the fermionic density. We derive truncated FRG flow equations for the fermionic and bosonic self-energies and for the three-legged vertices with two fermionic and one bosonic external legs. We consider two different cutoff schemes—cutoff in fermionic or bosonic propagators—in order to calculate the renormalized quasiparticle velocity and the dielectric function for an arbitrary number of Weyl nodes and the interaction strength. If we approximate the dielectric function by its static limit, our results for the velocity and the dielectric function are in good agreement with that of A. A. Abrikosov and S. D. Beneslavskiĭ [Sov. Phys. JETP 32, 699 (1971)] exhibiting slowly varying logarithmic momentum dependence for small momenta. We extend their result for an arbitrary number of Weyl nodes and finite frequency by evaluating the renormalized velocity in the presence of dynamic screening and calculate the wave function renormalization.
Rose, F.; Dupuis, N.
2018-05-01
We present an approximation scheme of the nonperturbative renormalization group that preserves the momentum dependence of correlation functions. This approximation scheme can be seen as a simple improvement of the local potential approximation (LPA) where the derivative terms in the effective action are promoted to arbitrary momentum-dependent functions. As in the LPA, the only field dependence comes from the effective potential, which allows us to solve the renormalization-group equations at a relatively modest numerical cost (as compared, e.g., to the Blaizot-Mendéz-Galain-Wschebor approximation scheme). As an application we consider the two-dimensional quantum O(N ) model at zero temperature. We discuss not only the two-point correlation function but also higher-order correlation functions such as the scalar susceptibility (which allows for an investigation of the "Higgs" amplitude mode) and the conductivity. In particular, we show how, using Padé approximants to perform the analytic continuation i ωn→ω +i 0+ of imaginary frequency correlation functions χ (i ωn) computed numerically from the renormalization-group equations, one can obtain spectral functions in the real-frequency domain.
Renormalization group flow of scalar models in gravity
International Nuclear Information System (INIS)
Guarnieri, Filippo
2014-01-01
In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.
Potts ferromagnet correlation length in hypercubic lattices: Renormalization - group approach
International Nuclear Information System (INIS)
Curado, E.M.F.; Hauser, P.R.
1984-01-01
Through a real space renormalization group approach, the q-state Potts ferromagnet correlation length on hierarchical lattices is calculated. These hierarchical lattices are build in order to simulate hypercubic lattices. The high-and-low temperature correlation length asymptotic behaviours tend (in the Ising case) to the Bravais lattice correlation length ones when the size of the hierarchical lattice cells tends to infinity. It is conjectured that the asymptotic behaviours several values of q and d (dimensionality) so obtained are correct. Numerical results are obtained for the full temperature range of the correlation length. (Author) [pt
Tensor renormalization group with randomized singular value decomposition
Morita, Satoshi; Igarashi, Ryo; Zhao, Hui-Hai; Kawashima, Naoki
2018-03-01
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.
Renormalization-group-invariant 1/N corrections to nontrival φ4 theory
International Nuclear Information System (INIS)
Smekal, L.v.; Langfeld, K.; Reinhardt, H.; Langbein, R.F.
1994-01-01
In the framework of path integral linearization techniques, the effective potential and the master field equation for massless φ 4 theory, in the modified loop expansion around the mean field, are derived up to next to leading order. In the O(N)-symmetric theory, these equations are equivalent to a subsummation of O(N) and order 1 diagrams. A renormalization prescription is proposed which is manifestly renormalization group invariant. The numerical results for the potential in next to leading order agree qualitatively well with the leading order ones. In particular, the nontrivial phase structure remains unchanged. Quantitatively, the corrections ar small for N much-gt 8, but even for N as small as one their essential effect is to modify the scaling coefficient β 0 in the Callan-Symanzik β function, in accordance with conventional loop expansions. The numerical results are best parametrized by scaling improved mean field formulas. Dimensional transmutation renders the overall (physical) mass scale M 0 , generated by a dynamical breaking of scale invariance, the only adjustable parameter of the theory. Renormalization group invariance of the numerical results is explicitly verified
Renormalization and effective lagrangians
International Nuclear Information System (INIS)
Polchinski, J.
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional lambda PHI 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed. (orig.)
Dynamical renormalization group resummation of finite temperature infrared divergences
International Nuclear Information System (INIS)
Boyanovsky, D.; Vega, H.J. de; Boyanovsky, D.; Simionato, M.; Holman, R.; Simionato, M.
1999-01-01
We introduce the method of dynamical renormalization group to study relaxation and damping out of equilibrium directly in real time and apply it to the study of infrared divergences in scalar QED. This method allows a consistent resummation of infrared effects associated with the exchange of quasistatic transverse photons and leads to anomalous logarithmic relaxation of the form e -αampersandhthinsp;Tampersandhthinsp;tampersandhthinsp;ln[t/t 0 ] for hard momentum charged excitations. This is in contrast with the usual quasiparticle interpretation of charged collective excitations at finite temperature in the sense of exponential relaxation of a narrow width resonance for which the width is the imaginary part of the self-energy on shell. In the case of narrow resonances away from thresholds, this approach leads to the usual exponential relaxation. The hard thermal loop resummation program is incorporated consistently into the dynamical renormalization group yielding a picture of relaxation and damping phenomena in a plasma in real time that transcends the conceptual limitations of the quasiparticle picture and other types of resummation schemes. copyright 1999 The American Physical Society
Holographic renormalization group and cosmology in theories with quasilocalized gravity
International Nuclear Information System (INIS)
Csaki, Csaba; Erlich, Joshua; Hollowood, Timothy J.; Terning, John
2001-01-01
We study the long distance behavior of brane theories with quasilocalized gravity. The five-dimensional (5D) effective theory at large scales follows from a holographic renormalization group flow. As intuitively expected, the graviton is effectively four dimensional at intermediate scales and becomes five dimensional at large scales. However, in the holographic effective theory the essentially 4D radion dominates at long distances and gives rise to scalar antigravity. The holographic description shows that at large distances the Gregory-Rubakov-Sibiryakov (GRS) model is equivalent to the model recently proposed by Dvali, Gabadadze, and Porrati (DGP), where a tensionless brane is embedded into 5D Minkowski space, with an additional induced 4D Einstein-Hilbert term on the brane. In the holographic description the radion of the GRS model is automatically localized on the tensionless brane, and provides the ghostlike field necessary to cancel the extra graviton polarization of the DGP model. Thus, there is a holographic duality between these theories. This analysis provides physical insight into how the GRS model works at intermediate scales; in particular it sheds light on the size of the width of the graviton resonance, and also demonstrates how the holographic renormalization group can be used as a practical tool for calculations
Source Localization by Entropic Inference and Backward Renormalization Group Priors
Directory of Open Access Journals (Sweden)
Nestor Caticha
2015-04-01
Full Text Available A systematic method of transferring information from coarser to finer resolution based on renormalization group (RG transformations is introduced. It permits building informative priors in finer scales from posteriors in coarser scales since, under some conditions, RG transformations in the space of hyperparameters can be inverted. These priors are updated using renormalized data into posteriors by Maximum Entropy. The resulting inference method, backward RG (BRG priors, is tested by doing simulations of a functional magnetic resonance imaging (fMRI experiment. Its results are compared with a Bayesian approach working in the finest available resolution. Using BRG priors sources can be partially identified even when signal to noise ratio levels are up to ~ -25dB improving vastly on the single step Bayesian approach. For low levels of noise the BRG prior is not an improvement over the single scale Bayesian method. Analysis of the histograms of hyperparameters can show how to distinguish if the method is failing, due to very high levels of noise, or if the identification of the sources is, at least partially possible.
Applications of the renormalization group approach to problems in quantum field theory
International Nuclear Information System (INIS)
Renken, R.L.
1985-01-01
The presence of fluctuations at many scales of length complicates theories of quantum fields. However, interest is often focused on the low-energy consequences of a theory rather than the short distance fluctuations. In the renormalization-group approach, one takes advantage of this by constructing an effective theory with identical low-energy behavior, but without short distance fluctuations. Three problems of this type are studied here. In chapter 1, an effective lagrangian is used to compute the low-energy consequences of theories of technicolor. Corrections to weak-interaction parameters are found to be small, but conceivably measurable. In chapter 2, the renormalization group approach is applied to second order phase transitions in lattice gauge theories such as the deconfining transition in the U(1) theory. A practical procedure for studying the critical behavior based on Monte Carlo renormalization group methods is described in detail; no numerical results are presented. Chapter 3 addresses the problem of computing the low-energy behavior of atoms directly from Schrodinger's equation. A straightforward approach is described, but is found to be impractical
Seiler, Christian; Evers, Ferdinand
2016-10-01
A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG flow is organized in the energy-domain rather than in k space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band structure, such as disordered metals or molecules. The energy-domain FRG (ɛ FRG) presented here accounts for Fermi-liquid corrections to quasiparticle energies and particle-hole excitations. It goes beyond the state of the art G W -BSE , because in ɛ FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the ɛ FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of ɛ FRG to the spinless disordered Hubbard model we calculate its phase boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S =1 /2 is also given.
Energy Technology Data Exchange (ETDEWEB)
Zinn-Justin, J
2003-08-01
In the quantum field theory the problem of infinite values has been solved empirically through a method called renormalization, this method is satisfying only in the framework of renormalization group. It is in the domain of statistical physics and continuous phase transitions that these issues are the easiest to discuss. Within the framework of a course in theoretical physics the author introduces the notions of continuous limits and universality in stochastic systems operating with a high number of freedom degrees. It is shown that quasi-Gaussian and mean field approximation are unable to describe phase transitions in a satisfying manner. A new concept is required: it is the notion of renormalization group whose fixed points allow us to understand universality beyond mean field. The renormalization group implies the idea that long distance correlations near the transition temperature might be described by a statistical field theory that is a quantum field in imaginary time. Various forms of renormalization group equations are presented and solved in particular boundary limits, namely for fields with high numbers of components near the dimensions 4 and 2. The particular case of exact renormalization group is also introduced. (A.C.)
Unique determination of the effective potential in terms of renormalization group functions
International Nuclear Information System (INIS)
Chishtie, F. A.; Hanif, T.; McKeon, D. G. C.; Steele, T. G.
2008-01-01
The perturbative effective potential V in the massless λφ 4 model with a global O(N) symmetry is uniquely determined to all orders by the renormalization group functions alone when the Coleman-Weinberg renormalization condition (d 4 V/dφ 4 )| φ=μ =λ is used, where μ represents the renormalization scale. Systematic methods are developed to express the n-loop effective potential in the Coleman-Weinberg scheme in terms of the known n-loop minimal-subtraction (MS) renormalization group functions. Moreover, it also proves possible to sum the leading- and subsequent-to-leading-logarithm contributions to V. An essential element of this analysis is a conversion of the renormalization group functions in the Coleman-Weinberg scheme to the renormalization group functions in the MS scheme. As an example, the explicit five-loop effective potential is obtained from the known five-loop MS renormalization group functions and we explicitly sum the leading-logarithm, next-to-leading-logarithm, and further subleading-logarithm contributions to V. Extensions of these results to massless scalar QED are also presented. Because massless scalar QED has two couplings, conversion of the renormalization group functions from the MS scheme to the Coleman-Weinberg scheme requires the use of multiscale renormalization group methods.
Numerical renormalization group method for entanglement negativity at finite temperature
Shim, Jeongmin; Sim, H.-S.; Lee, Seung-Sup B.
2018-04-01
We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature and a sudden death at high temperature. In the Anderson model, the charge fluctuation of the impurity contributes to the negativity even at zero temperature when the on-site Coulomb repulsion of the impurity is finite, while at low temperature the negativity between the impurity spin and the bath exhibits the same power-law scaling behavior as in the Kondo model.
High Precision Renormalization Group Study of the Roughening Transition
Hasenbusch, M; Pinn, K
1994-01-01
We confirm the Kosterlitz-Thouless scenario of the roughening transition for three different Solid-On-Solid models: the Discrete Gaussian model, the Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with standard (cosine) action. The method is based on a matching of the renormalization group flow of the candidate models with the flow of a bona fide KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are performed using efficient cluster algorithms. We obtain high precision estimates for the critical couplings and other non-universal quantities. For the XY model with cosine action our critical coupling estimate is $\\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and $K_R^{ASOS}=0.8061(3)$, respectively.
A geometric renormalization group in discrete quantum space-time
International Nuclear Information System (INIS)
Requardt, Manfred
2003-01-01
We model quantum space-time on the Planck scale as dynamical networks of elementary relations or time dependent random graphs, the time dependence being an effect of the underlying dynamical network laws. We formulate a kind of geometric renormalization group on these (random) networks leading to a hierarchy of increasingly coarse-grained networks of overlapping lumps. We provide arguments that this process may generate a fixed limit phase, representing our continuous space-time on a mesoscopic or macroscopic scale, provided that the underlying discrete geometry is critical in a specific sense (geometric long range order). Our point of view is corroborated by a series of analytic and numerical results, which allow us to keep track of the geometric changes, taking place on the various scales of the resolution of space-time. Of particular conceptual importance are the notions of dimension of such random systems on the various scales and the notion of geometric criticality
Mutual information, neural networks and the renormalization group
Koch-Janusz, Maciej; Ringel, Zohar
2018-06-01
Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains `slow' degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.
Renormalization group theory for percolation in time-varying networks.
Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M
2018-05-22
Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.
Irreversibility of world-sheet renormalization group flow
International Nuclear Information System (INIS)
Oliynyk, T.; Suneeta, V.; Woolgar, E.
2005-01-01
We demonstrate the irreversibility of a wide class of world-sheet renormalization group (RG) flows to first order in α ' in string theory. Our techniques draw on the mathematics of Ricci flows, adapted to asymptotically flat target manifolds. In the case of somewhere-negative scalar curvature (of the target space), we give a proof by constructing an entropy that increases monotonically along the flow, based on Perelman's Ricci flow entropy. One consequence is the absence of periodic solutions, and we are able to give a second, direct proof of this. If the scalar curvature is everywhere positive, we instead construct a regularized volume to provide an entropy for the flow. Our results are, in a sense, the analogue of Zamolodchikov's c-theorem for world-sheet RG flows on noncompact spacetimes (though our entropy is not the Zamolodchikov C-function)
Functional renormalization group study of the Anderson–Holstein model
International Nuclear Information System (INIS)
Laakso, M A; Kennes, D M; Jakobs, S G; Meden, V
2014-01-01
We present a comprehensive study of the spectral and transport properties in the Anderson–Holstein model both in and out of equilibrium using the functional renormalization group (fRG). We show how the previously established machinery of Matsubara and Keldysh fRG can be extended to include the local phonon mode. Based on the analysis of spectral properties in equilibrium we identify different regimes depending on the strength of the electron–phonon interaction and the frequency of the phonon mode. We supplement these considerations with analytical results from the Kondo model. We also calculate the nonlinear differential conductance through the Anderson–Holstein quantum dot and find clear signatures of the presence of the phonon mode. (paper)
Higgs boson, renormalization group, and naturalness in cosmology
International Nuclear Information System (INIS)
Barvinsky, A.O.; Kamenshchik, A.Yu.; Kiefer, C.; Starobinsky, A.A.; Steinwachs, C.F.
2012-01-01
We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Wu, Wei [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China); Beijing Computational Science Research Center, Beijing 100193 (China); Xu, Jing-Bo, E-mail: xujb@zju.edu.cn [Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University, Hangzhou 310027 (China)
2017-01-30
We investigate the performances of quantum coherence and multipartite entanglement close to the quantum critical point of a one-dimensional anisotropic spin-1/2 XXZ spin chain by employing the real-space quantum renormalization group approach. It is shown that the quantum criticality of XXZ spin chain can be revealed by the singular behaviors of the first derivatives of renormalized quantum coherence and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized quantum coherence and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical point of XXZ spin chain. - Highlights: • The QPT of XXZ chain is studied by renormalization group. • The renormalized coherence and multiparticle entanglement is investigated. • Scaling laws of renormalized coherence and multiparticle entanglement are revealed.
Renormalization group improved Yennie-Frautschi-Suura theory for Z0 physics
International Nuclear Information System (INIS)
Ward, B.F.L.
1987-06-01
Described is a recently developed renormalization group improved version of the program of Yennie, Frautschi and Suura for the exponentiation of infrared divergences in Abelian gauge theories. Particular attention is paid to the relevance of this renormalization group improved exponentiation to Z 0 physics at the SLC and LEP
Renormalization Group Invariance of the Pole Mass in the Multi-Higgs System
Kim, Chungku
2018-06-01
We have investigated the renormalization group running of the pole mass in the multi-Higgs theory in two different types of gauge fixing conditions. The pole mass, when expressed in terms of the Lagrangian parameters, turns out to be invariant under the renormalization group with the beta and gamma functions of the symmetric phase.
de Albuquerque, Douglas F.; Santos-Silva, Edimilson; Moreno, N. O.
2009-10-01
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
Energy Technology Data Exchange (ETDEWEB)
Albuquerque, Douglas F. de [Departamento de Matematica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil)], E-mail: douglas@ufs.br; Santos-Silva, Edimilson [Departamento de Matematica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil); Moreno, N.O. [Departamento de Fisica, Universidade Federal de Sergipe, 49100-000 Sao Cristovao, SE (Brazil)
2009-10-15
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents {nu} for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
International Nuclear Information System (INIS)
Albuquerque, Douglas F. de; Santos-Silva, Edimilson; Moreno, N.O.
2009-01-01
In this letter we employing the effective-field renormalization group (EFRG) to study the Ising model with nearest neighbors to obtain the reduced critical temperature and exponents ν for bi- and three-dimensional lattices by increasing cluster scheme by extending recent works. The technique follows up the same strategy of the mean field renormalization group (MFRG) by introducing an alternative way for constructing classical effective-field equations of state takes on rigorous Ising spin identities.
Antonov, N. V.; Gulitskiy, N. M.; Kostenko, M. M.; Malyshev, A. V.
2018-03-01
In this paper we consider the model of incompressible fluid described by the stochastic Navier-Stokes equation with finite correlation time of a random force. Inertial-range asymptotic behavior of fully developed turbulence is studied by means of the field theoretic renormalization group within the one-loop approximation. It is corroborated that regardless of the values of model parameters and initial data the inertial-range behavior of the model is described by the limiting case of vanishing correlation time. This indicates that the Galilean symmetry of the model violated by the "colored" random force is restored in the inertial range. This regime corresponds to the only nontrivial fixed point of the renormalization group equation. The stability of this point depends on the relation between the exponents in the energy spectrum E ∝k1 -y and the dispersion law ω ∝k2 -η . The second analyzed problem is the passive advection of a scalar field by this velocity ensemble. Correlation functions of the scalar field exhibit anomalous scaling behavior in the inertial-convective range. We demonstrate that in accordance with Kolmogorov's hypothesis of the local symmetry restoration the main contribution to the operator product expansion is given by the isotropic operator, while anisotropic terms should be considered only as corrections.
Asymptotic behavior of composite-particle form factors and the renormalization group
International Nuclear Information System (INIS)
Duncan, A.; Mueller, A.H.
1980-01-01
Composite-particle form factors are studied in the limit of large momentum transfer Q. It is shown that in models with spinor constituents and either scalar or gauge vector gluons, the meson electromagnetic form factor factorizes at large Q 2 and is given by independent light-cone expansions on the initial and final meson legs. The coefficient functions are shown to satisfy a Callan-Symanzik equation. When specialized to quantum chromodynamics, this equation leads to the asymptotic formula of Brodsky and Lepage for the pion electromagnetic form factor. The nucleon form factors G/sub M/(Q 2 ), G/sub E/(Q 2 ) are also considered. It is shown that momentum flows which contribute to subdominant logarithms in G/sub M/(Q 2 ) vitiate a conventional renormalization-group interpretation for this form factor. For large Q 2 , the electric form factor G/sub E/(Q 2 ) fails to factorize, so that a renormalization-group treatment seems even more unlikely in this case
A renormalization group scaling analysis for compressible two-phase flow
International Nuclear Information System (INIS)
Chen, Y.; Deng, Y.; Glimm, J.; Li, G.; Zhang, Q.; Sharp, D.H.
1993-01-01
Computational solutions to the Rayleigh--Taylor fluid mixing problem, as modeled by the two-fluid two-dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone suggests fixed-point behavior. The profile of statistical quantities within the mixing zone exhibit self-similarity under fixed-point scaling to a limited degree. The effect of compressibility is also examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predicted from a renormalization group fixed-point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit
Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model
Energy Technology Data Exchange (ETDEWEB)
Meloni, Davide [Dipartimento di Matematica e Fisica, Università di Roma Tre,Via della Vasca Navale 84, 00146 Rome (Italy); Ohlsson, Tommy; Riad, Stella [Department of Physics, School of Engineering Sciences,KTH Royal Institute of Technology - AlbaNova University Center,Roslagstullsbacken 21, 106 91 Stockholm (Sweden)
2017-03-08
We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10{sub H}, 120{sub H}, and 126{sub H} representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M{sub I}. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10{sub H} and 126{sub H} representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.
Perturbative renormalization of composite operators via flow equations. Pt. 2
International Nuclear Information System (INIS)
Keller, G.; Kopper, C.
1993-01-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive Φ 4 4 . The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.)
Alternating chain with Hubbard-type interactions: renormalization group analysis
International Nuclear Information System (INIS)
Buzatu, F. D.; Jackeli, G.
1998-01-01
A large amount of work has been devoted to the study of alternating chains for a better understanding of the high-T c superconductivity mechanism. The same phenomenon renewed the interest in the Hubbard model and in its one-dimensional extensions. In this work we investigate, using the Renormalization Group (RG) method, the effect of the Hubbard-type interactions on the ground-state properties of a chain with alternating on-site atomic energies. The one-particle Hamiltonian in the tight binding approximation corresponding to an alternating chain with two nonequivalent sites per unit cell can be diagonalized by a canonical transformation; one gets a two band model. The Hubbard-type interactions give rise to both intra- and inter-band couplings; however, if the gap between the two bands is sufficiently large and the system is more than half-filled, as for the CuO 3 chain occurring in high-T c superconductors, the last ones can be neglected in describing the low energy physics. We restrict our considerations to the Hubbard-type interactions (upper band) in the particular case of alternating on-site energies and equal hopping amplitudes. The standard RG analysis (second order) is done in terms of the g-constants describing the elementary processes of forward, backward and Umklapp scatterings: their expressions are obtained by evaluating the Hubbard-type interactions (upper band) at the Fermi points. Using the scaling to the exact soluble models Tomonaga-Luttinger and Luther-Emery, we can predict the low energy physics of our system. The ground-state phase diagrams in terms of the model parameters and at arbitrary band filling are determined, where four types of instabilities have been considered: Charge Density Waves (CDW), Spin Density Waves (SDW), Singlet Superconductivity (SS) and Triplet Superconductivity (TS). The 3/4-filled case in terms of some renormalized Hubbard constants is presented. The relevance of our analysis to the case of the undistorted 3/4-filled Cu
Renormalization group evolution of the universal theories EFT
International Nuclear Information System (INIS)
Wells, James D.; Zhang, Zhengkang
2016-01-01
The conventional oblique parameters analyses of precision electroweak data can be consistently cast in the modern framework of the Standard Model effective field theory (SMEFT) when restrictions are imposed on the SMEFT parameter space so that it describes universal theories. However, the usefulness of such analyses is challenged by the fact that universal theories at the scale of new physics, where they are matched onto the SMEFT, can flow to nonuniversal theories with renormalization group (RG) evolution down to the electroweak scale, where precision observables are measured. The departure from universal theories at the electroweak scale is not arbitrary, but dictated by the universal parameters at the matching scale. But to define oblique parameters, and more generally universal parameters at the electroweak scale that directly map onto observables, additional prescriptions are needed for the treatment of RG-induced nonuniversal effects. We perform a RG analysis of the SMEFT description of universal theories, and discuss the impact of RG on simplified, universal-theories-motivated approaches to fitting precision electroweak and Higgs data.
Renormalization group method in the theory of dynamical systems
International Nuclear Information System (INIS)
Sinai, Y.G.; Khanin, K.M.
1988-01-01
One of the most important events in the theory of dynamical systems for the last decade has become a wide penetration of ideas and renormalization group methods (RG) into this traditional field of mathematical physics. RG-method has been one of the main tools in statistical physics and it has proved to be rather effective while solving problems of the theory of dynamical systems referring to new types of bifurcations (see further). As in statistical mechanics the application of the RG-method is of great interest in the neighborhood of the critical point concerning the order-chaos transition. First the RG-method was applied in the pioneering papers dedicated to the appearance of a stochastical regime as a result of infinite sequences of period doubling bifurcations. At present this stochasticity mechanism is the most studied one and many papers deal with it. The study of the so-called intermittency phenomenon was the next example of application of the RG-method, i.e. the study of such a situation where the domains of the stochastical and regular behavior do alternate along a trajectory of the dynamical system
Renormalization group approach to a p-wave superconducting model
International Nuclear Information System (INIS)
Continentino, Mucio A.; Deus, Fernanda; Caldas, Heron
2014-01-01
We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.
Driven similarity renormalization group: Third-order multireference perturbation theory.
Li, Chenyang; Evangelista, Francesco A
2017-03-28
A third-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT3) approach is presented. The DSRG-MRPT3 method has several appealing features: (a) it is intruder free, (b) it is size consistent, (c) it leads to a non-iterative algorithm with O(N 6 ) scaling, and (d) it includes reference relaxation effects. The DSRG-MRPT3 scheme is benchmarked on the potential energy curves of F 2 , H 2 O 2 , C 2 H 6 , and N 2 along the F-F, O-O, C-C, and N-N bond dissociation coordinates, respectively. The nonparallelism errors of DSRG-MRPT3 are consistent with those of complete active space third-order perturbation theory and multireference configuration interaction with singles and doubles and show significant improvements over those obtained from DSRG second-order multireference perturbation theory. Our efficient implementation of the DSRG-MRPT3 based on factorized electron repulsion integrals enables studies of medium-sized open-shell organic compounds. This point is demonstrated with computations of the singlet-triplet splitting (Δ ST =E T -E S ) of 9,10-anthracyne. At the DSRG-MRPT3 level of theory, our best estimate of the adiabatic Δ ST is 3.9 kcal mol -1 , a value that is within 0.1 kcal mol -1 from multireference coupled cluster results.
Interleaved numerical renormalization group as an efficient multiband impurity solver
Stadler, K. M.; Mitchell, A. K.; von Delft, J.; Weichselbaum, A.
2016-06-01
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a "Wilson chain." It was shown recently that Wilson chains for different electronic species can be interleaved by use of a modified discretization, dramatically increasing the numerical efficiency of the RG scheme [Phys. Rev. B 89, 121105(R) (2014), 10.1103/PhysRevB.89.121105]. Here we systematically examine the accuracy and efficiency of the "interleaved" NRG (iNRG) method in the context of the single impurity Anderson model, the two-channel Kondo model, and a three-channel Anderson-Hund model. The performance of iNRG is explicitly compared with "standard" NRG (sNRG): when the average number of states kept per iteration is the same in both calculations, the accuracy of iNRG is equivalent to that of sNRG but the computational costs are significantly lower in iNRG when the same symmetries are exploited. Although iNRG weakly breaks SU(N ) channel symmetry (if present), both accuracy and numerical cost are entirely competitive with sNRG exploiting full symmetries. iNRG is therefore shown to be a viable and technically simple alternative to sNRG for high-symmetry models. Moreover, iNRG can be used to solve a range of lower-symmetry multiband problems that are inaccessible to sNRG.
Critical asymmetry in renormalization group theory for fluids.
Zhao, Wei; Wu, Liang; Wang, Long; Li, Liyan; Cai, Jun
2013-06-21
The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.
Renormalization group study of the melting of a two-dimensional system of collapsing hard disks
Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu. D.; Tsiok, E. N.; Chumakov, E. S.
2017-06-01
We consider the melting of a two-dimensional system of collapsing hard disks (a system with a hard-disk potential to which a repulsive step is added) for different values of the repulsive-step width. We calculate the system phase diagram by the method of the density functional in crystallization theory using equations of the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory to determine the lines of stability with respect to the dissociation of dislocation pairs, which corresponds to the continuous transition from the solid to the hexatic phase. We show that the crystal phase can melt via a continuous transition at low densities (the transition to the hexatic phase) with a subsequent transition from the hexatic phase to the isotropic liquid and via a first-order transition. Using the solution of renormalization group equations with the presence of singular defects (dislocations) in the system taken into account, we consider the influence of the renormalization of the elastic moduli on the form of the phase diagram.
Renormalization-group flow of the effective action of cosmological large-scale structures
Floerchinger, Stefan
2017-01-01
Following an approach of Matarrese and Pietroni, we derive the functional renormalization group (RG) flow of the effective action of cosmological large-scale structures. Perturbative solutions of this RG flow equation are shown to be consistent with standard cosmological perturbation theory. Non-perturbative approximate solutions can be obtained by truncating the a priori infinite set of possible effective actions to a finite subspace. Using for the truncated effective action a form dictated by dissipative fluid dynamics, we derive RG flow equations for the scale dependence of the effective viscosity and sound velocity of non-interacting dark matter, and we solve them numerically. Physically, the effective viscosity and sound velocity account for the interactions of long-wavelength fluctuations with the spectrum of smaller-scale perturbations. We find that the RG flow exhibits an attractor behaviour in the IR that significantly reduces the dependence of the effective viscosity and sound velocity on the input ...
Renormalization group analysis of B →π form factors with B -meson light-cone sum rules
Shen, Yue-Long; Wei, Yan-Bing; Lü, Cai-Dian
2018-03-01
Within the framework of the B -meson light-cone sum rules, we review the calculation of radiative corrections to the three B →π transition form factors at leading power in Λ /mb. To resum large logarithmic terms, we perform the complete renormalization group evolution of the correlation function. We employ the integral transformation which diagonalizes evolution equations of the jet function and the B -meson light-cone distribution amplitude to solve these evolution equations and obtain renormalization group improved sum rules for the B →π form factors. Results of the form factors are extrapolated to the whole physical q2 region and are compared with that of other approaches. The effect of B -meson three-particle light-cone distribution amplitudes, which will contribute to the form factors at next-to-leading power in Λ /mb at tree level, is not considered in this paper.
The Kadanoff lower-bound variational renormalization group applied to an SU(2) lattice spin model
International Nuclear Information System (INIS)
Thorleifsson, G.; Damgaard, P.H.
1990-07-01
We apply the variational lower-bound Renormalization Group transformation of Kadanoff to an SU(2) lattice spin model in 2 and 3 dimensions. Even in the one-hypercube framework of this renormalization group transformation the present model is characterised by having an infinite basis of fundamental operators. We investigate whether the lower-bound variational renormalization group transformation yields results stable under truncations of this operator basis. Our results show that for this particular spin model this is not the case. (orig.)
Directory of Open Access Journals (Sweden)
Uwe C. Täuber
2014-04-01
Full Text Available The universal critical behavior of the driven-dissipative nonequilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex-valued Landau-Ginzburg functional, which captures the near critical nonequilibrium dynamics, and generalizes model A for classical relaxational dynamics with nonconserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest nontrivial order in the dimensional ε expansion about the upper critical dimension d_{c}=4 and establish the emergence of a novel universal scaling exponent associated with the nonequilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (subdiffusive model B with complex coefficients.
Classical open-string field theory: A∞-algebra, renormalization group and boundary states
International Nuclear Information System (INIS)
Nakatsu, Toshio
2002-01-01
We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles
de Albuquerque, Douglas F.; Fittipaldi, I. P.
1994-05-01
A unified effective-field renormalization-group framework (EFRG) for both quenched bond- and site-diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean-field renormalization-group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective-field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two- and three-dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size-cluster version, provides results that correctly distinguishes those lattices that have the same coordination number, but differ in dimensionality or geometry.
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Renormalization group analysis of order parameter fluctuations in fermionic superfluids
International Nuclear Information System (INIS)
Obert, Benjamin
2014-01-01
In this work fluctuation effects in two interacting fermion systems exhibiting fermionic s-wave superfluidity are analyzed with a modern renormalization group method. A description in terms of a fermion-boson theory allows an investigation of order parameter fluctuations already on the one-loop level. In the first project a quantum phase transition between a semimetal and a s-wave superfluid in a Dirac cone model is studied. The interplay between fermions and quantum critical fluctuations close to and at the quantum critical point at zero and finite temperatures are studied within a coupled fermion-boson theory. At the quantum critical point non-Fermi liquid and non-Gaussian behaviour emerge. Close to criticality several quantities as the susceptibility show a power law behaviour with critical exponents. We find an infinite correlation length in the entire semimetallic ground state also away from the quantum critical point. In the second project, the ground state of an s-wave fermionic superfluid is investigated. Here, the mutual interplay between fermions and order parameter fluctuations is studied, especially the impact of massless Goldstone fluctuations, which occur due to spontaneous breaking of the continuous U(1)-symmetry. Fermionic gap and bosonic order parameter are distinguished. Furthermore, the bosonic order parameter is decomposed in transverse and longitudinal fluctuations. The mixing between transverse and longitudinal fluctuations is included in our description. Within a simple truncation of the fermion-boson RG flow, we describe the fermion-boson theory for the first time in a consistent manner. Several singularities appear due the Goldstone fluctuations, which partially cancel due to symmetry. Our RG flow captures the correct infrared asymptotics of the system, where the collective excitations act as an interacting Bose gas. Lowest order Ward identities and the massless Goldstone mode are fulfilled in our truncation.
The functional renormalization group for interacting quantum systems with spin-orbit interaction
International Nuclear Information System (INIS)
Grap, Stephan Michael
2013-01-01
We studied the influence of spin-orbit interaction (SOI) in interacting low dimensional quantum systems at zero temperature within the framework of the functional renormalization group (fRG). Among the several types of spin-orbit interaction the so-called Rashba spin-orbit interaction is especially intriguing for future spintronic applications as it may be tuned via external electric fields. We investigated its effect on the low energy physics of an interacting quantum wire in an applied Zeeman field which is modeled as a generalization of the extended Hubbard model. To this end we performed a renormalization group study of the two particle interaction, including the SOI and the Zeeman field exactly on the single particle level. Considering the resulting two band model, we formulated the RG equations for the two particle vertex keeping the full band structure as well as the non trivial momentum dependence of the low energy two particle scattering processes. In order to solve these equations numerically we defined criteria that allowed us to classify whether a given set of initial conditions flows towards the strongly coupled regime. We found regions in the models parameter space where a weak coupling method as the fRG is applicable and it is possible to calculate additional quantities of interest. Furthermore we analyzed the effect of the Rashba SOI on the properties of an interacting multi level quantum dot coupled to two semi in nite leads. Of special interest was the interplay with a Zeeman field and its orientation with respect to the SOI term. We found a renormalization of the spin-orbit energy which is an experimental quantity used to asses SOI effects in transport measurements, as well as renormalized effective g factors used to describe the Zeeman field dependence. In particular in asymmetrically coupled systems the large parameter space allows for rich physics which we studied by means of the linear conductance obtained via the generalized Landauer
Merzlikin, Boris S.; Shapiro, Ilya L.; Wipf, Andreas; Zanusso, Omar
2017-12-01
Using covariant methods, we construct and explore the Wetterich equation for a nonminimal coupling F (ϕ )R of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered nonminimal coupling ξ ϕ2R as a special case. We consider the truncations without and with scale- and field-dependent wave-function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the nonminimal coupling in the symmetric and spontaneously broken phases with vanishing and nonvanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension d =4 .
International Nuclear Information System (INIS)
Nandori, I.; Jentschura, U.D.; Soff, G.; Sailer, K.
2004-01-01
Renormalization-group (RG) flow equations have been derived for the generalized sine-Gordon model (GSGM) and the Coulomb gas (CG) in d≥3 of dimensions by means of the Wegner-Houghton method, and by way of the real-space RG approach. The UV scaling laws determined by the leading-order terms of the flow equations are in qualitative agreement for all dimensions d≥3, independent of the dimensionality, and in sharp contrast to the special case d=2. For the 4-dimensional GSGM it is demonstrated explicitly (by numerical calculations) that the blocked potential tends to a constant effective potential in the infrared limit, satisfying the requirements of periodicity and convexity. The comparison of the RG flows for the three-dimensional GSGM, the CG, and the vortex-loop gas reveals a significant dependence on the renormalization schemes and the approximations used
Introduction to the renormalization group study in relativistic quantum field theory
International Nuclear Information System (INIS)
Mignaco, J.A.; Roditi, I.
1985-01-01
An introduction to the renormalization group approach in relativistic quantum field theories is presented, beginning with a little historical about the subject. Further, this problem is discussed from the point of view of the perturbation theory. (L.C.) [pt
Two-and three-dimension Potts magnetism in the renormalization group approximation
International Nuclear Information System (INIS)
Silva, L.R. da.
1985-01-01
Through a real space Renormalization Group (RG) technique we discuss the criticality of various physical systems, calculate order parameters for geometrical problems and analyse convergence aspects of the RG theory. (author) [pt
TOPICAL REVIEW: Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model
Meurice, Y.
2007-06-01
We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice. We introduce the HM and show that its large group of symmetry simplifies drastically the blockspinning procedure. Several equivalent forms of the recursion formula are presented with unified notations. Rigourous and numerical results concerning the recursion formula are summarized. It is pointed out that the recursion formula of the HM is inequivalent to both Wilson's approximate recursion formula and Polchinski's equation in the local potential approximation (despite the very small difference with the exponents of the latter). We draw a comparison between the RG of the HM and functional RG equations in the local potential approximation. The construction of the linear and nonlinear scaling variables is discussed in an operational way. We describe the calculation of non-universal critical amplitudes in terms of the scaling variables of two fixed points. This question appears as a problem of interpolation between these fixed points. Universal amplitude ratios are calculated. We discuss the large-N limit and the complex singularities of the critical potential calculable in this limit. The interpolation between the HM and more conventional lattice models is presented as a symmetry breaking problem. We briefly introduce models with an approximate supersymmetry. One important goal of this review is to present a configuration space counterpart, suitable for lattice formulations, of functional RG equations formulated in momentum space (often called exact RG equations and abbreviated ERGE).
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage
1976-01-01
The transverse correlation range ξ and the susceptibility in the critical region has been measured by neutron scattering. A special technique required to resolve the superdiverging longitudinal correlation range has been utilized. The results for ξ together with existing specific-heat data are in...... are in remarkable agreement with the renormalization group theory of systems with marginal dimensionality. The ratio between the susceptibility amplitudes above and below Tc was found to be 2 in accordance with renormalization-group and meanfield theory....
Renormalization of supersymmetric theories
International Nuclear Information System (INIS)
Pierce, D.M.
1998-06-01
The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M W and sin 2 θ eff . He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses
In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
Truncation effects in the functional renormalization group study of spontaneous symmetry breaking
International Nuclear Information System (INIS)
Defenu, N.; Mati, P.; Márián, I.G.; Nándori, I.; Trombettoni, A.
2015-01-01
We study the occurrence of spontaneous symmetry breaking (SSB) for O(N) models using functional renormalization group techniques. We show that even the local potential approximation (LPA) when treated exactly is sufficient to give qualitatively correct results for systems with continuous symmetry, in agreement with the Mermin-Wagner theorem and its extension to systems with fractional dimensions. For general N (including the Ising model N=1) we study the solutions of the LPA equations for various truncations around the zero field using a finite number of terms (and different regulators), showing that SSB always occurs even where it should not. The SSB is signalled by Wilson-Fisher fixed points which for any truncation are shown to stay on the line defined by vanishing mass beta functions.
International Nuclear Information System (INIS)
Dias, S.A.
1985-01-01
The transformation law of truncated pertubation theory observables under changes of renormalization scheme is deduced. Based on this, a criticism of the calculus of the moments of structure functions in deep inelastic scattering, obtaining that the A 2 coefficient not renormalization group invariant is done. The PMS criterion is used to optimize the perturbative productions of the moments, truncated to 2nd order. (author) [pt
Renormalization-group decimation technique for spectra, wave-functions and density of states
International Nuclear Information System (INIS)
Wiecko, C.; Roman, E.
1983-09-01
The Renormalization Group decimation technique is very useful for problems described by 1-d nearest neighbour tight-binding model with or without translational invariance. We show how spectra, wave-functions and density of states can be calculated with little numerical work from the renormalized coefficients upon iteration. The results of this new procedure are verified using the model of Soukoulis and Economou. (author)
Teodorovich, E. V.
2018-03-01
In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.
Golden mean renormalization for a generalized Harper equation: The Ketoja-Satija orchid
International Nuclear Information System (INIS)
Mestel, B.D.; Osbaldestin, A.H.
2004-01-01
We provide a rigorous analysis of the fluctuations of localized eigenstates in a generalized Harper equation with golden mean flux and with next-nearest-neighbor interactions. For next-nearest-neighbor interaction above a critical threshold, these self-similar fluctuations are characterized by orbits of a renormalization operator on a universal strange attractor, whose projection was dubbed the ''orchid'' by Ketoja and Satija [Phys. Rev. Lett. 75, 2762 (1995)]. We show that the attractor is given essentially by an embedding of a subshift of finite type, and give a description of its periodic orbits
On the renormalization group flow in two dimensional superconformal models
International Nuclear Information System (INIS)
Ahn, Changrim; Stanishkov, Marian
2014-01-01
We extend the results on the RG flow in the next to leading order to the case of the supersymmetric minimal models SM p for p≫1. We explain how to compute the NS and Ramond fields conformal blocks in the leading order in 1/p and follow the renormalization scheme proposed in [1]. As a result we obtained the anomalous dimensions of certain NS and Ramond fields. It turns out that the linear combination expressing the infrared limit of these fields in term of the IR theory SM p−2 is exactly the same as those of the nonsupersymmetric minimal theory
Renormalization group flow of entanglement entropy on spheres
Energy Technology Data Exchange (ETDEWEB)
Ben-Ami, Omer; Carmi, Dean [Raymond and Beverly Sackler Faculty of Exact Sciences School of Physics and Astronomy,Tel-Aviv University, Ramat-Aviv 69978 (Israel); Smolkin, Michael [Center for Theoretical Physics and Department of Physics,University of California, Berkeley, CA 94720 (United States)
2015-08-12
We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the bare couplings and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in d=2,3,4. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal ‘area law’ for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.
Renormalization group aspects of 3-dimensional Pure U(1) lattice gauge theory
International Nuclear Information System (INIS)
Gopfert, M.; Mack, G.
1983-01-01
A few surprises in a recent study of the 3-dimensional pure U(1) lattice gauge theory model, from the point of view of the renormalization group theory, are discussed. Since the gauge group U(1) of this model is abelian, the model is subject to KramersWannier duality transformation. One obtains a ferromagnet with a global symmetry group Z. The duality transformation shows that the surface tension alpha of the model equals the strong tension of the U(1) gauge model. A theorem to represent the true asymptotic behaviour of alpha is derived. A second theorem considers the correlation functions. Discrepiancies between the theorems result in a solution that ''is regarded as a catastrophe'' in renormalization group theory. A lesson is drawn: To choose a good block spin in a renormalization group procedure, know what the low lying excitations of the theory are, to avoid integrating some of them by mischief
Collision group and renormalization of the Boltzmann collision integral
Saveliev, V. L.; Nanbu, K.
2002-05-01
On the basis of a recently discovered collision group [V. L. Saveliev, in Rarefied Gas Dynamics: 22nd International Symposium, edited by T. J. Bartel and M. Gallis, AIP Conf. Proc. No. 585 (AIP, Melville, NY, 2001), p. 101], the Boltzmann collision integral is exactly rewritten in two parts. The first part describes the scattering of particles with small angles. In this part the infinity due to the infinite cross sections is extracted from the Boltzmann collision integral. Moreover, the Boltzmann collision integral is represented as a divergence of the flow in velocity space. Owing to this, the role of collisions in the kinetic equation can be interpreted in terms of the nonlocal friction force that depends on the distribution function.
Renormalization of the fragmentation equation: Exact self-similar solutions and turbulent cascades
Saveliev, V. L.; Gorokhovski, M. A.
2012-12-01
Using an approach developed earlier for renormalization of the Boltzmann collision integral [Saveliev and Nanbu, Phys. Rev. E1539-375510.1103/PhysRevE.65.051205 65, 051205 (2002)], we derive an exact divergence form for the fragmentation operator. Then we reduce the fragmentation equation to the continuity equation in size space, with the flux given explicitly. This allows us to obtain self-similar solutions and to find the integral of motion for these solutions (we call it the bare flux). We show how these solutions can be applied as a description of cascade processes in three- and two-dimensional turbulence. We also suggested an empirical cascade model of impact fragmentation of brittle materials.
International Nuclear Information System (INIS)
Lenaghan, J.T.; Rischke, D.H.
2000-01-01
The temperature dependence of the sigma meson and pion masses is studied in the framework of the O(N ) model. The Cornwall-Jackiw-Tomboulis formalism is applied to derive gap equations for the masses in the Hartree and large-N approximations. Renormalization of the gap equations is carried out within the cut-off and counter-term renormalization schemes. A consistent renormalization of the gap equations within the cut-off scheme is found to be possible only in the large-N approximation and for a finite value of the cut-off. On the other hand, the counter-term scheme allows for a consistent renormalization of both the large-N and Hartree approximations. In these approximations, the meson masses at a given nonzero temperature depend in general on the choice of the cut-off or renormalization scale. As an application, we also discuss the in-medium on-shell decay widths for sigma mesons and pions at rest. (author)
Hanasoge, Shravan; Agarwal, Umang; Tandon, Kunj; Koelman, J. M. Vianney A.
2017-09-01
Determining the pressure differential required to achieve a desired flow rate in a porous medium requires solving Darcy's law, a Laplace-like equation, with a spatially varying tensor permeability. In various scenarios, the permeability coefficient is sampled at high spatial resolution, which makes solving Darcy's equation numerically prohibitively expensive. As a consequence, much effort has gone into creating upscaled or low-resolution effective models of the coefficient while ensuring that the estimated flow rate is well reproduced, bringing to the fore the classic tradeoff between computational cost and numerical accuracy. Here we perform a statistical study to characterize the relative success of upscaling methods on a large sample of permeability coefficients that are above the percolation threshold. We introduce a technique based on mode-elimination renormalization group theory (MG) to build coarse-scale permeability coefficients. Comparing the results with coefficients upscaled using other methods, we find that MG is consistently more accurate, particularly due to its ability to address the tensorial nature of the coefficients. MG places a low computational demand, in the manner in which we have implemented it, and accurate flow-rate estimates are obtained when using MG-upscaled permeabilities that approach or are beyond the percolation threshold.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Closed-form irreducible differential formulations of the Wilson renormalization group
International Nuclear Information System (INIS)
Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.
1983-01-01
We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
Energy Technology Data Exchange (ETDEWEB)
Hergert, H., E-mail: hergert@nscl.msu.edu [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics, The Ohio State University, Columbus, OH 43210 (United States); Bogner, S.K., E-mail: bogner@nscl.msu.edu [National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); Morris, T.D., E-mail: morrist@nscl.msu.edu [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States); National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824 (United States); Schwenk, A., E-mail: schwenk@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt (Germany); Tsukiyama, K., E-mail: tsuki.kr@gmail.com [Center for Nuclear Study, Graduate School of Science, University of Tokyo, Hongo, Tokyo, 113-0033 (Japan)
2016-03-21
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
The In-Medium Similarity Renormalization Group: A novel ab initio method for nuclei
International Nuclear Information System (INIS)
Hergert, H.; Bogner, S.K.; Morris, T.D.; Schwenk, A.; Tsukiyama, K.
2016-01-01
We present a comprehensive review of the In-Medium Similarity Renormalization Group (IM-SRG), a novel ab initio method for nuclei. The IM-SRG employs a continuous unitary transformation of the many-body Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem. Starting from a pedagogical introduction of the underlying concepts, the IM-SRG flow equations are developed for systems with and without explicit spherical symmetry. We study different IM-SRG generators that achieve the desired decoupling, and how they affect the details of the IM-SRG flow. Based on calculations of closed-shell nuclei, we assess possible truncations for closing the system of flow equations in practical applications, as well as choices of the reference state. We discuss the issue of center-of-mass factorization and demonstrate that the IM-SRG ground-state wave function exhibits an approximate decoupling of intrinsic and center-of-mass degrees of freedom, similar to Coupled Cluster (CC) wave functions. To put the IM-SRG in context with other many-body methods, in particular many-body perturbation theory and non-perturbative approaches like CC, a detailed perturbative analysis of the IM-SRG flow equations is carried out. We conclude with a discussion of ongoing developments, including IM-SRG calculations with three-nucleon forces, the multi-reference IM-SRG for open-shell nuclei, first non-perturbative derivations of shell-model interactions, and the consistent evolution of operators in the IM-SRG. We dedicate this review to the memory of Gerry Brown, one of the pioneers of many-body calculations of nuclei.
A density matrix renormalization group study of low-lying excitations ...
Indian Academy of Sciences (India)
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...
Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus
2015-01-28
We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.
DEFF Research Database (Denmark)
Hedegård, Erik D.; Knecht, Stefan; Kielberg, Jesper Skau
2015-01-01
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electroncorrelation...... effects in multiconfigurational electronic structure problems....
Phase diagram of the Hubbard model with arbitrary band filling: renormalization group approach
International Nuclear Information System (INIS)
Cannas, Sergio A.; Cordoba Univ. Nacional; Tsallis, Constantino.
1991-01-01
The finite temperature phase diagram of the Hubbard model in d = 2 and d = 3 is calculated for arbitrary values of the parameter U/t and chemical potential μ using a quantum real space renormalization group. Evidence for a ferromagnetic phase at low temperatures is presented. (author). 15 refs., 5 figs
Scaling laws, renormalization group flow and the continuum limit in non-compact lattice QED
International Nuclear Information System (INIS)
Goeckeler, M.; Horsley, R.; Rakow, P.; Schierholz, G.; Sommer, R.
1992-01-01
We investigate the ultra-violet behavior of non-compact lattice QED with light staggered fermions. The main question is whether QED is a non-trivial theory in the continuum limit, and if not, what is its range of validity as a low-energy theory. Perhaps the limited range of validity could offer an explanation of why the fine-structure constant is so small. Non-compact QED undergoes a second-order chiral phase transition at strong coupling, at which the continuum limit can be taken. We examine the phase diagram and the critical behavior of the theory in detail. Moreover, we address the question as to whether QED confines in the chirally broken phase. This is done by investigating the potential between static external charges. We then compute the renormalized charge and derive the Callan-Symanzik β-function in the critical region. No ultra-violet stable zero is found. Instead, we find that the evolution of charge is well described by renormalized perturbation theory, and that the renormalized charge vanishes at the critical point. The consequence is that QED can only be regarded as a cut-off theory. We evaluate the maximum value of the cut-off as a function of the renormalized charge. Next, we compute the masses of fermion-antifermion composite states. The scaling behavior of these masses is well described by an effective action with mean-field critical exponents plus logarithmic corrections. This indicates that also the matter sector of the theory is non-interacting. Finally, we investigate and compare the renormalization group flow of different quantities. Altogether, we find that QED is a valid theory only for samll renormalized charges. (orig.)
Ab initio excited states from the in-medium similarity renormalization group
Parzuchowski, N. M.; Morris, T. D.; Bogner, S. K.
2017-04-01
We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of 1 p 1 h excitations) becomes exact for a subset of eigenvalues. In the second approach, EOM techniques are applied to the IMSRG ground-state-decoupled Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two dimensions and the closed-shell nuclei 16O and 22O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but it is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster calculations. This work paves the way for more interesting applications of the EOM-IMSRG approach to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within one or two nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.
Renormalization Group Flows from Holography-Supersymmetry and a c-Theorem
Freedman, D.Z.; Pilch, K.; Warner, N.P.
1999-01-01
We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function...
International Nuclear Information System (INIS)
Antonov, N V
2006-01-01
Recent progress on the anomalous scaling in models of turbulent heat and mass transport is reviewed with the emphasis on the approach based on the field-theoretic renormalization group (RG) and operator product expansion (OPE). In that approach, the anomalous scaling is established as a consequence of the existence in the corresponding field-theoretic models of an infinite number of 'dangerous' composite fields (operators) with negative critical dimensions, which are identified with the anomalous exponents. This allows one to calculate the exponents in a systematic perturbation expansion, similar to the ε expansion in the theory of critical phenomena. The RG and OPE approach is presented in a self-contained way for the example of a passive scalar field (temperature, concentration of an impurity, etc) advected by a self-similar Gaussian velocity ensemble with vanishing correlation time, the so-called Kraichnan's rapid-change model, where the anomalous exponents are known up to order O(ε 3 ). Effects of anisotropy, compressibility and the correlation time of the velocity field are discussed. Passive advection by non-Gaussian velocity field governed by the stochastic Navier-Stokes equation and passively advected vector (e.g. magnetic) fields are considered
A renormalization group invariant line and an infrared attractive top-Higgs mass relation
International Nuclear Information System (INIS)
Schrempp, B.; Schrempp, F.
1992-10-01
The renormalization group equations (RGE's) of the Standard Model at one loop in terms of the gauge couplings g 1,2,3, the top Yukawa coupling g t and the scalar self coupling λ are reexamined. For g 1,2 = 0, the general solution of the RGE's is obtained analytically in terms of an interesting special solution for the ratio λ/g 2 t as function of the ratio g 2 t /g 2 3 which i) represents an RG invariant line which is strongly infrared attractive ii) interpolates all known quasi-fixed points and iii) is finite for large g 2 t /g 2 3 (ultraviolet limit). All essential features survive for g 1,2 ≠ 0. The invariant line translates into an infrared attractive top-Higgs mass relation, which e.g. associates to the top masses m t = 130/145/200 GeV the Higgs masses m H ≅ 68-90/103-115/207 GeV, respectively. (orig.)
Li, Chenyang; Verma, Prakash; Hannon, Kevin P.; Evangelista, Francesco A.
2017-08-01
We propose an economical state-specific approach to evaluate electronic excitation energies based on the driven similarity renormalization group truncated to second order (DSRG-PT2). Starting from a closed-shell Hartree-Fock wave function, a model space is constructed that includes all single or single and double excitations within a given set of active orbitals. The resulting VCIS-DSRG-PT2 and VCISD-DSRG-PT2 methods are introduced and benchmarked on a set of 28 organic molecules [M. Schreiber et al., J. Chem. Phys. 128, 134110 (2008)]. Taking CC3 results as reference values, mean absolute deviations of 0.32 and 0.22 eV are observed for VCIS-DSRG-PT2 and VCISD-DSRG-PT2 excitation energies, respectively. Overall, VCIS-DSRG-PT2 yields results with accuracy comparable to those from time-dependent density functional theory using the B3LYP functional, while VCISD-DSRG-PT2 gives excitation energies comparable to those from equation-of-motion coupled cluster with singles and doubles.
Holography as a highly efficient renormalization group flow. I. Rephrasing gravity
Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan
2016-07-01
We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.
Advanced density matrix renormalization group method for nuclear structure calculations
Czech Academy of Sciences Publication Activity Database
Legeza, Ö.; Veis, Libor; Poves, A.; Dukelsky, J.
2015-01-01
Roč. 92, č. 5 (2015), 051303 ISSN 0556-2813 Institutional support: RVO:61388955 Keywords : INITIO QUANTUM- CHEMISTRY * GROUP ALGORITHM * SHELL-MODEL Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.146, year: 2015
Perturbative and constructive renormalization
International Nuclear Information System (INIS)
Veiga, P.A. Faria da
2000-01-01
These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)
On the renormalization group perspective of α-attractors
Energy Technology Data Exchange (ETDEWEB)
Narain, Gaurav, E-mail: gaunarain@itp.ac.cn [Kavli Institute for Theoretical Physics China (KITPC), Key Laboratory of Theoretical Physics, Institute of Theoretical Physics (ITP), Chinese Academy of Sciences -CAS, Beijing 100190 (China)
2017-10-01
In this short paper we outline a recipe for the reconstruction of F ( R ) gravity starting from single field inflationary potentials in the Einstein frame. For simple potentials one can compute the explicit form of F ( R ), whilst for more involved examples one gets a parametric form of F ( R ). The F ( R ) reconstruction algorithm is used to study various examples: power-law φ {sup n} , exponential and α -attractors. In each case it is seen that for large R (corresponding to large value of inflaton field), F ( R ) ∼ R {sup 2}. For the case of α -attractors F ( R ) ∼ R {sup 2} for all values of inflaton field (for all values of R ) as α → 0. For generic inflaton potential V (φ), it is seen that if V {sup '}/ V →0 (for some φ) then the corresponding F ( R ) ∼ R {sup 2}. We then study α-attractors in more detail using non-perturbative renormalisation group methods to analyse the reconstructed F ( R ). It is seen that α →0 is an ultraviolet stable fixed point of the renormalisation group trajectories.
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-14
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).
Renormalization group and finite size effects in scalar lattice field theories
International Nuclear Information System (INIS)
Bernreuther, W.; Goeckeler, M.
1988-01-01
Binder's phenomenological renormalization group is studied in the context of the O(N)-symmetric euclidean lattice φ 4 theory in dimensions d ≤ 4. By means of the field theoretical formulation of the renormalization group we analyse suitable ratios of Green functions on finite lattices in the limit where the dimensionless lattice length L >> 1 and where the dimensionless bare mass approaches the critical point of the corresponding infinite volume model. If the infrared-stable fixed point which controls this limit is a simple zero of the β-function we are led to formulae which allow the extraction of the critical exponents ν and η. For the gaussian fixed point in four dimensions, discussed as a known example for a multiple zero of the β-function, we derive for these ratios the leading logarithmic corrections to mean field scaling. (orig.)
Quantum gravity and the functional renormalization group the road towards asymptotic safety
Reuter, Martin
2018-01-01
During the past two decades the gravitational asymptotic safety scenario has undergone a major transition from an exotic possibility to a serious contender for a realistic theory of quantum gravity. It aims at a mathematically consistent quantum description of the gravitational interaction and the geometry of spacetime within the realm of quantum field theory, which keeps its predictive power at the highest energies. This volume provides a self-contained pedagogical introduction to asymptotic safety, and introduces the functional renormalization group techniques used in its investigation, along with the requisite computational techniques. The foundational chapters are followed by an accessible summary of the results obtained so far. It is the first detailed exposition of asymptotic safety, providing a unique introduction to quantum gravity and it assumes no previous familiarity with the renormalization group. It serves as an important resource for both practising researchers and graduate students entering thi...
Functional renormalization group and Kohn-Sham scheme in density functional theory
Liang, Haozhao; Niu, Yifei; Hatsuda, Tetsuo
2018-04-01
Deriving accurate energy density functional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy density functional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in density functional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.
International Nuclear Information System (INIS)
Bergstroem, Johannes; Ohlsson, Tommy; Zhang He
2011-01-01
We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).
Implementation and assessment of the renormalization group (Rng) k - ε model in gothic
International Nuclear Information System (INIS)
Analytis, G.Th.
2001-01-01
In GOTHIC, the standard k - ε model is used to model turbulence. In an attempt to enhance the turbulence modelling capabilities of the code for simulation of mixing driven by highly buoyant discharges, we implemented the Renormalization Group (RNG) k - ε model. This model which for the time being, is only implemented in the ''gas'' phase, was tested with different simple test-problems and its predictions were compared to the corresponding ones obtained when the standard k - ε model was used. (author)
Piomelli, Ugo; Zang, Thomas A.; Speziale, Charles G.; Lund, Thomas S.
1990-01-01
An eddy viscosity model based on the renormalization group theory of Yakhot and Orszag (1986) is applied to the large-eddy simulation of transition in a flat-plate boundary layer. The simulation predicts with satisfactory accuracy the mean velocity and Reynolds stress profiles, as well as the development of the important scales of motion. The evolution of the structures characteristic of the nonlinear stages of transition is also predicted reasonably well.
A confining and asymptotically free solution for the renormalization group invariant charge
International Nuclear Information System (INIS)
Kellett, B.H.
1978-01-01
The central role of the invariant charge in applications of the renormalization group to quantum chromodynamics is discussed. The general structure of the invariant charge is examined, and it is shown to be a non-singular function of q 2 for all finite non-zero q 2 . At q 2 = 0 and q 2 = +or- infinity shows that QCD is asymptotically free. Some applications of these general results are discussed
Competition between direct interaction and Kondo effect: Renormalization-group approach
International Nuclear Information System (INIS)
Allub, R.
1988-03-01
Via the Wilson renormalization-group approach, the effect of the competition between direct interaction (J L ) and Kondo coupling is studied, in the magnetic susceptibility of a model with two different magnetic impurities. For the ferromagnetic interaction (J L > 0) between the localized impurities, we find a magnetic ground state and a divergent susceptibility at low temperatures. For (J L < 0), two different Kondo temperatures and a non-magnetic ground state are distinguished. (author). 12 refs, 1 fig
A renormalization group study of persistent current in a quasiperiodic ring
Energy Technology Data Exchange (ETDEWEB)
Dutta, Paramita [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata-700 108 (India); Karmakar, S.N. [Theoretical Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata-700 064 (India)
2014-04-01
We propose a real-space renormalization group approach for evaluating persistent current in a multi-channel quasiperiodic Fibonacci tight-binding ring based on a Green's function formalism. Unlike the traditional methods, the present scheme provides a powerful tool for the theoretical description of persistent current with a very high degree of accuracy in large periodic and quasiperiodic rings, even in the micron scale range, which emphasizes the merit of this work.
Directory of Open Access Journals (Sweden)
Antonov N.V.
2016-01-01
Full Text Available We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t′/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa–Kardar model is irrelevant and to the “pure” Hwa–Kardar model (the advection is irrelevant. For the special case ξ = 2(4 − d/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.
Renormalization group summation of Laplace QCD sum rules for scalar gluon currents
Directory of Open Access Journals (Sweden)
Farrukh Chishtie
2016-03-01
Full Text Available We employ renormalization group (RG summation techniques to obtain portions of Laplace QCD sum rules for scalar gluon currents beyond the order to which they have been explicitly calculated. The first two of these sum rules are considered in some detail, and it is shown that they have significantly less dependence on the renormalization scale parameter μ2 once the RG summation is used to extend the perturbative results. Using the sum rules, we then compute the bound on the scalar glueball mass and demonstrate that the 3 and 4-Loop perturbative results form lower and upper bounds to their RG summed counterparts. We further demonstrate improved convergence of the RG summed expressions with respect to perturbative results.
Absence of renormalization group pathologies near the critical temperature. Two examples
International Nuclear Information System (INIS)
Haller, K.; Kennedy, T.
1996-01-01
We consider real-space renormalization group transformations for Ising-type systems which are formally defined by where T(σ, σ') is a probability kernel, i.e., Σ σ' T(σ, σ') = 1, for every configuration σ. For each choice of the block spin configuration σ', let μ σ' , be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional to T(σ, σ') exp[ -H(σ)]. We give a condition which is sufficient to imply that the renormalized Hamiltonian H' is defined. Roughly speaking, the condition is that the collection of measures μ σ' is in the high-temperature phase uniformly in the block spin configuration σ'. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacing b = 2 on the square lattice with β c and the Kadanoff transformation with parameter p on the triangular lattice in a subset of the β, p plane that includes values of β greater than β c
International Nuclear Information System (INIS)
Tsallis, C.; Levy, S.V.F.
1979-05-01
Two different renormalization-group approaches are used to determine approximate solutions for the paramagnetic-ferromagnetic transition line of the square-lattice bond-dilute first-neighbour-interaction Ising model. (Author) [pt
Lima, J. P. De; Gonçalves, L. L.
The critical dynamics of the isotropic XY-model on the one-dimensional superlattice is considered in the framework of the position space renormalization group theory. The decimation transformation is introduced by considering the equations of motion of the operators associated to the excitations of the system, and it corresponds to an extension of the procedure introduced by Stinchcombe and dos Santos (J. Phys. A18, L597 (1985)) for the homogeneous lattice. The dispersion relation is obtained exactly and the static and dynamic scaling forms are explicitly determined. The dynamic critical exponent is also obtained and it is shown that it is identical to the one of the XY-model on the homogeneous chain.
International Nuclear Information System (INIS)
Werner, Gerhard
2013-01-01
The topic of this paper will be addressed in three stages: I will first review currently prominent theoretical conceptualizations of the neurobiology of consciousness and, where appropriate, identify ill-advised and flawed notions in theoretical neuroscience that may impede viewing consciousness as a phenomenon in the physics of brain. In this context, I will also introduce relevant facts that tend not to receive adequate attention in much of the current consciousness discourse. Next, I will review the evidence that accrued in the last decade that identifies the resting brain as being in a state of criticality. In the framework of state phase dynamics of statistical physics, this observational evidence also entails that the resting brain is poised at the brink of a second order phase transition. On this basis, I will in the third stage propose applying the framework of the Renormalization Group to viewing consciousness as a phenomenon in statistical physics. In physics, concepts of phase space transitions and the Renormalization Group are powerful tools for interpreting phenomena involving many scales of length and time in complex systems. The significance of these concepts lies in their accounting for the emergence of different levels of new collective behaviors in complex systems, each level with its distinct macroscopic physics, organization, and laws, as a new pattern of reality. In this framework, I propose to view subjectivity as the symbolic description of the physical brain state of consciousness that emerges as one of the levels of phase transitions of the brain-body-environment system, along the trajectory of Renormalization Group Transformations
A novel functional renormalization group framework for gauge theories and gravity
Energy Technology Data Exchange (ETDEWEB)
Codello, Alessandro
2010-07-01
In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for k{yields}{infinity} and the standard effective action for k{yields}0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NL{sigma}M) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or
Renormalization group analysis of the global properties of a strange attractor
International Nuclear Information System (INIS)
Kadanoff, L.P.
1986-01-01
This paper considers the circle map at the special point: the one at which there is a trajectory with a golden mean winding number and at which the map just fails to be invertable at one point on the circle. The invariant density of this trajectory has fractal properties. Previous work has suggested that the global behavior of this fractal can be effectively analyzed using a kind of partition function formalism to generate an f versus Σ curve. In this paper the partition function is obtained by using a renormalization group approach
Renormalization-group studies of antiferromagnetic chains. I. Nearest-neighbor interactions
International Nuclear Information System (INIS)
Rabin, J.M.
1980-01-01
The real-space renormalization-group method introduced by workers at the Stanford Linear Accelerator Center (SLAC) is used to study one-dimensional antiferromagnetic chains at zero temperature. Calculations using three-site blocks (for the Heisenberg-Ising model) and two-site blocks (for the isotropic Heisenberg model) are compared with exact results. In connection with the two-site calculation a duality transformation is introduced under which the isotropic Heisenberg model is self-dual. Such duality transformations can be defined for models other than those considered here, and may be useful in various block-spin calculations
A functional renormalization group application to the scanning tunneling microscopy experiment
Directory of Open Access Journals (Sweden)
José Juan Ramos Cárdenas
2015-12-01
Full Text Available We present a study of a system composed of a scanning tunneling microscope (STM tip coupled to an absorbed impurity on a host surface using the functional renormalization group (FRG. We include the effect of the STM tip as a correction to the self-energy in addition to the usual contribution of the host surface in the wide band limit. We calculate the differential conductance curves at two different lateral distances from the quantum impurity and find good qualitative agreement with STM experiments where the differential conductance curves evolve from an antiresonance to a Lorentzian shape.
Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension
International Nuclear Information System (INIS)
Levermore, C.D.; Nadler, W.; Stein, D.L.
1995-01-01
We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice
Schmitteckert, Peter
2018-04-01
We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.
Exploring excited eigenstates of many-body systems using the functional renormalization group
Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph
2018-05-01
We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.
DEFF Research Database (Denmark)
Codello, Alessandro; Tonero, Alberto
2016-01-01
We present a simple and consistent way to compute correlation functions in interacting theories with nontrivial phase diagram. As an example we show how to consistently compute the four-point function in three dimensional Z2-scalar theories. The idea is to perform the path integral by weighting...... the momentum modes that contribute to it according to their renormalization group (RG) relevance, i.e. we weight each mode according to the value of the running couplings at that scale. In this way, we are able to encode in a loop computation the information regarding the RG trajectory along which we...
The renormalization group study of the effective theory of lattice QED
International Nuclear Information System (INIS)
Sugiyama, Y.
1988-01-01
The compact U(1) lattice gauge theory with massless fermions (Lattice QED) is studied through the effective model analytically, using the renormalization group method. The obtained effective model is the local boson field system with non-local interactions. The authors study the existence of non-trivial fixed point and its scaling behavior. This fixed point seems to be tri-critical. Such fixed point is interpreted in terms of the original Lattice QED model, and the results are consistent with the Monte Calro study
Dynamical symmetry breaking of the electroweak interactions and the renormalization group
International Nuclear Information System (INIS)
Hill, C.T.
1990-08-01
We discuss dynamical symmetry breaking with an emphasis on the renormalization group as the key tool to obtaining reliable predictions. In particular we discuss the mechanism for breaking the electroweak interactions which relies upon the formation of condensates involving the conventional quarks and leptons. Such a scheme indicates that the top quark is heavy, greater than or of order 200 GeV, and gives further predictions for the Higgs boson mass. We also briefly describe recent attempts to incorporate a 4th generation in a more natural scheme. 13 refs., 3 figs., 1 tab
Renormalization group study of the one-dimensional quantum Potts model
International Nuclear Information System (INIS)
Solyom, J.; Pfeuty, P.
1981-01-01
The phase transition of the classical two-dimensional Potts model, in particular the order of the transition as the number of components q increases, is studied by constructing renormalization group transformations on the equivalent one-dimensional quatum problem. It is shown that the block transformation with two sites per cell indicates the existence of a critical qsub(c) separating the small q and large q regions with different critical behaviours. The physically accessible fixed point for q>qsub(c) is a discontinuity fixed point where the specific heat exponent α=1 and therefore the transition is of first order. (author)
Break-collapse method for resistor networks-renormalization group applications
International Nuclear Information System (INIS)
Tsallis, C.; Coniglio, A.; Redner, S.
1982-01-01
The break-collapse method recently introduced for the q-state Potts model is adapted for resistor networks. This method greatly simplifies the calculation of the conductance of an arbitrary two-terminal d-dimensional array of conductances, obviating the use of either Kirchhoff's laws or the star-triangle or similiar transformations. Related properties are discussed as well. An illustrative real-space renormalization-group treatment of the random resistor problem on the square lattice is presented; satisfactory results are obtained. (Author) [pt
International Nuclear Information System (INIS)
Riera, R.; Oliveira, P.M.C. de; Chaves, C.M.G.F.; Queiroz, S.L.A. de.
1980-04-01
A real-space renormalization group approach for the bond percolation problem in a square lattice with first- and second- neighbour bonds is proposed. The respective probabilities are treated, as independent variables. Two types of cells are constructed. In one of them the lattice is considered as two interpenetrating sublattices, first-neighbour bonds playing the role of intersublattice links. This allows the calculation of both critical exponents ν and γ, without resorting to any external field. Values found for the critical indices are in good agreement with data available in the literature. The phase diagram in parameter space is also obtained in each case. (Author) [pt
Renormalization group critical frontier of the three-dimensional bond-dilute Ising ferromagnet
International Nuclear Information System (INIS)
Chao, N.-C.; Schwaccheim, G.; Tsallis, C.
1981-01-01
The critical frontier (as well as the thermal type critical exponents) associated to the quenched bond-dilute spin - 1/2 Ising ferromagnet in the simple cubic lattice is approximately calculated within a real space renormalization group framework in two different versions. Both lead to qualitatively satisfactory critical frontiers, although one of them provides an unphysical fixed point (which seem to be related to the three-dimensionality of the system) besides the expected pure ones; its effects tend to disappear for increasingly large clusters. Through an extrapolation procedure the (unknown) critical frontier is approximately located. (Author) [pt
Renormalization of self-consistent Schwinger-Dyson equations at finite temperature
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2002-01-01
We show that Dyson resummation schemes based on Baym's Φ-derivable approximations can be renormalized with counter term structures solely defined on the vacuum level. First applications to the self-consistent solution of the sunset self-energy in φ 4 -theory are presented. (orig.)
A bulk localized state and new holographic renormalization group flow in 3D spin-3 gravity
Nakayama, Ryuichi; Suzuki, Tomotaka
2018-04-01
We construct a localized state of a scalar field in 3D spin-3 gravity. 3D spin-3 gravity is thought to be holographically dual to W3-extended CFT on a boundary at infinity. It is known that while W3 algebra is a nonlinear algebra, in the limit of large central charge c a linear finite-dimensional subalgebra generated by Wn (n = 0,±1,±2) and Ln (n = 0,±1) is singled out. The localized state is constructed in terms of these generators. To write down an equation of motion for a scalar field which is satisfied by this localized state, it is necessary to introduce new variables for an internal space α±, β±, γ, in addition to ordinary coordinates x± and y. The higher-dimensional space, which combines the bulk space-time with the “internal space,” which is an analog of superspace in supersymmetric theory, is introduced. The “physical bulk space-time” is a 3D hypersurface with constant α±, β± and γ embedded in this space. We will work in Poincaré coordinates of AdS space and consider W-quasi-primary operators Φh(x+) with a conformal weight h in the boundary and study two and three point functions of W-quasi-primary operators transformed as eix+L‑1heβ+W‑1hΦh(0)e‑β+W‑1he‑ix+L‑1h. Here, Lnh and Wnh are sl(3,R) generators in the hyperbolic basis for Poincaré coordinates. It is shown that in the β+ →∞ limit, the conformal weight changes to a new value h‧ = h/2. This may be regarded as a Renormalization Group (RG) flow. It is argued that this RG flow will be triggered by terms ΔS ∝ β+W ‑1h + β‑W¯ ‑1h added to the action.
Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach
Grusdt, Fabian; Seetharam, Kushal; Shchadilova, Yulia; Demler, Eugene
2018-03-01
When a mobile impurity interacts with a surrounding bath of bosons, it forms a polaron. Numerous methods have been developed to calculate how the energy and the effective mass of the polaron are renormalized by the medium for equilibrium situations. Here, we address the much less studied nonequilibrium regime and investigate how polarons form dynamically in time. To this end, we develop a time-dependent renormalization-group approach which allows calculations of all dynamical properties of the system and takes into account the effects of quantum fluctuations in the polaron cloud. We apply this method to calculate trajectories of polarons following a sudden quench of the impurity-boson interaction strength, revealing how the polaronic cloud around the impurity forms in time. Such trajectories provide additional information about the polaron's properties which are challenging to extract directly from the spectral function measured experimentally using ultracold atoms. At strong couplings, our calculations predict the appearance of trajectories where the impurity wavers back at intermediate times as a result of quantum fluctuations. Our method is applicable to a broader class of nonequilibrium problems. As a check, we also apply it to calculate the spectral function and find good agreement with experimental results. At very strong couplings, we predict that quantum fluctuations lead to the appearance of a dark continuum with strongly suppressed spectral weight at low energies. While our calculations start from an effective Fröhlich Hamiltonian describing impurities in a three-dimensional Bose-Einstein condensate, we also calculate the effects of additional terms in the Hamiltonian beyond the Fröhlich paradigm. We demonstrate that the main effect of these additional terms on the attractive side of a Feshbach resonance is to renormalize the coupling strength of the effective Fröhlich model.
Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group
de Sousa, J. Ricardo; Fittipaldi, I. P.
1994-05-01
A real-space effective-field renormalization-group method (ERFG) recently derived for computing critical properties of Ising spins is extended to treat the quantum spin-1/2 anisotropic Heisenberg model. The formalism is based on a generalized but approximate Callen-Suzuki spin relation and utilizes a convenient differential operator expansion technique. The method is illustrated in several lattice structures by employing its simplest approximation version in which clusters with one (N'=1) and two (N=2) spins are used. The results are compared with those obtained from the standard mean-field (MFRG) and Migdal-Kadanoff (MKRG) renormalization-group treatments and it is shown that this technique leads to rather accurate results. It is shown that, in contrast with the MFRG and MKRG predictions, the EFRG, besides correctly distinguishing the geometries of different lattice structures, also provides a vanishing critical temperature for all two-dimensional lattices in the isotropic Heisenberg limit. For the simple cubic lattice, the dependence of the transition temperature Tc with the exchange anisotropy parameter Δ [i.e., Tc(Δ)], and the resulting value for the critical thermal crossover exponent φ [i.e., Tc≂Tc(0)+AΔ1/φ ] are in quite good agreement with results available in the literature in which more sophisticated treatments are used.
Renormalization group improved bottom mass from {Upsilon} sum rules at NNLL order
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Hoang, Andre H.; Stahlhofen, Maximilian [Wien Univ. (Austria). Fakultaet fuer Physik; Ruiz-Femenia, Pedro [Wien Univ. (Austria). Fakultaet fuer Physik; Valencia Univ. - CSIC (Spain). IFIC
2012-09-15
We determine the bottom quark mass from non-relativistic large-n {Upsilon} sum rules with renormalization group improvement at next-to-next-to-leading logarithmic order. We compute the theoretical moments within the vNRQCD formalism and account for the summation of powers of the Coulomb singularities as well as of logarithmic terms proportional to powers of {alpha}{sub s} ln(n). The renormalization group improvement leads to a substantial stabilization of the theoretical moments compared to previous fixed-order analyses, which did not account for the systematic treatment of the logarithmic {alpha}{sub s} ln(n) terms, and allows for reliable single moment fits. For the current world average of the strong coupling ({alpha}{sub s}(M{sub Z})=0.1183{+-}0.0010) we obtain M{sub b}{sup 1S}=4.755{+-}0.057{sub pert} {+-}0.009{sub {alpha}{sub s}}{+-}0.003{sub exp} GeV for the bottom 1S mass and anti m{sub b}(anti m{sub b})=4.235{+-}0.055{sub pert}{+-}0.003{sub exp} GeV for the bottom MS mass, where we have quoted the perturbative error and the uncertainties from the strong coupling and the experimental data.
Rück, Marlon; Reuther, Johannes
2018-04-01
We implement an extension of the pseudofermion functional renormalization group method for quantum spin systems that takes into account two-loop diagrammatic contributions. An efficient numerical treatment of the additional terms is achieved within a nested graph construction which recombines different one-loop interaction channels. In order to be fully self-consistent with respect to self-energy corrections, we also include certain three-loop terms of Katanin type. We first apply this formalism to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and benchmark our results against the previous one-loop plus Katanin approach. Even though the renormalization group (RG) equations undergo significant modifications when including the two-loop terms, the magnetic phase diagram, comprising Néel ordered and collinear ordered phases separated by a magnetically disordered regime, remains remarkably unchanged. Only the boundary position between the disordered and the collinear phases is found to be moderately affected by two-loop terms. On the other hand, critical RG scales, which we associate with critical temperatures Tc, are reduced by a factor of ˜2 indicating that the two-loop diagrams play a significant role in enforcing the Mermin-Wagner theorem. Improved estimates for critical temperatures are also obtained for the Heisenberg ferromagnet on the three-dimensional simple cubic lattice where errors in Tc are reduced by ˜34 % . These findings have important implications for the quantum phase diagrams calculated within the previous one-loop plus Katanin approach which turn out to be already well converged.
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
Renormalization in few body nuclear physics
Energy Technology Data Exchange (ETDEWEB)
Tomio, L.; Biswas, R. [Instituto de Fisica Teorica, UNESP, 01405-900 Sao Paulo (Brazil); Delfino, A. [Instituto de Fisica, Universidade Federal Fluminenese, Niteroi (Brazil); Frederico, T. [Instituto Tecnologico de Aeronautica, CTA 12228-900 Sao Jose dos Campos (Brazil)
2001-09-01
Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the {sup 3}S{sub l} -{sup 3} D{sub 1} states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three
Renormalization in few body nuclear physics
International Nuclear Information System (INIS)
Tomio, L.; Biswas, R.; Delfino, A.; Frederico, T.
2001-01-01
Full text: Renormalized fixed-point Hamiltonians are formulated for systems described by interactions that originally contain point-like singularities (as the Dirac delta and/or its derivatives). The approach was developed considering a renormalization scheme for a few-nucleon interaction, that relies on a subtracted T-matrix equation. The fixed-point Hamiltonian contains the renormalized coefficients/operators that carry the physical information of the quantum mechanical system, as well as all the necessary counterterms that make finite the scattering amplitude. It is also behind the renormalization group invariance of quantum mechanics. The renormalization procedure, via subtracted kernel, was first applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. Considering only one scaling parameter, the results that were obtained show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. In this example, we noticed that the mixing parameter of the 3 S l - 3 D 1 states is the most sensible observable related to the renormalization scale. The above approach, where the nonrelativistic scattering equation with singular interaction is renormalized through a subtraction procedure at a given energy scale, lead us to propose a scheme to formulate renormalized (fixed- point) Hamiltonians in quantum mechanics. We illustrate the numerical diagonalization of the regularized form of the fixed-point Hamiltonian for a two-body system with a Yukawa plus a Dirac-delta interaction. The eigenvalues for the system are shown to be stable in the infinite momentum cutoff. In another example, we also derive the explicit form of the renormalized potential for an example of four-term singular bare interaction. Application of this renormalization scheme to three-body halo nuclei is also
Energy Technology Data Exchange (ETDEWEB)
Weyer, Holger
2010-12-17
We analyze the conceptual role of background independence in the application of the effective average action to quantum gravity. Insisting on a background independent nonperturbative renormalization group (RG) flow the coarse graining operation must be defined in terms of an unspecified variable metric since no rigid metric of a fixed background spacetime is available. This leads to an extra field dependence in the functional RG equation and a significantly different RG ow in comparison to the standard flow equation with a rigid metric in the mode cutoff. The background independent RG flow can possess a non-Gaussian fixed point, for instance, even though the corresponding standard one does not. We demonstrate the importance of this universal, essentially kinematical effect by computing the RG flow of Quantum Einstein Gravity (QEG) in the ''conformally reduced'' theory which discards all degrees of freedom contained in the metric except the conformal one. The conformally reduced Einstein-Hilbert approximation has exactly the same qualitative properties as in the full Einstein-Hilbert truncation. In particular it possesses the non-Gaussian fixed point which is necessary for asymptotic safety. Without the extra field dependence the resulting RG flow is that of a simple {phi}{sup 4}-theory. We employ the Local Potential Approximation for the conformal factor to generalize the RG flow on an infinite dimensional theory space. Again we find a Gaussian as well as a non-Gaussian fixed point which provides further evidence for the viability of the asymptotic safety scenario. The analog of the invariant cubic in the curvature which spoils perturbative renormalizability is seen to be unproblematic for the asymptotic safety of the conformally reduced theory. The scaling fields and dimensions of both fixed points are obtained explicitly and possible implications for the predictivity of the theory are discussed. Since the RG flow depends on the topology of the
Cleaver, G.; Espinosa, J.R.; Everett, L.L.; Langacker, P.; Wang, J.
1999-01-01
We continue the investigation of the physics implications of a class of flat directions for a prototype quasi-realistic free fermionic string model (CHL5), building upon the results of the previous paper in which the complete mass spectrum and effective trilinear couplings of the observable sector were calculated to all orders in the superpotential. We introduce soft supersymmetry breaking mass parameters into the model, and investigate the gauge symmetry breaking patterns and the renormalization group analysis for two representative flat directions, which leave an additional $U(1)'$ as well as the SM gauge group unbroken at the string scale. We study symmetry breaking patterns that lead to a phenomenologically acceptable $Z-Z'$ hierarchy, $M_{Z^{'}} \\sim {\\cal O}(1~{\\rm TeV})$ and $ 10^{12}~{\\rm GeV}$ for electroweak and intermediate scale $U(1)^{'}$ symmetry breaking, respectively, and the associated mass spectra after electroweak symmetry breaking. The fermion mass spectrum exhibits unrealistic features, i...
The two-loop renormalization of general quantum field theories
International Nuclear Information System (INIS)
Damme, R.M.J. van.
1984-01-01
This thesis provides a general method to compute all first order corrections to the renormalization group equations. This requires the computation of the first perturbative corrections to the renormalization group β-functions. These corrections are described by Feynman diagrams with two loops. The two-loop renormalization is treated for an arbitrary renormalization field theory. Two cases are considered: 1. the Yukawa sector; 2. the gauge coupling and the scalar potential. In a final section, the breakdown of unitarity in the dimensional reduction scheme is discussed. (Auth.)
Scale-invariant feature extraction of neural network and renormalization group flow
Iso, Satoshi; Shiba, Shotaro; Yokoo, Sumito
2018-05-01
Theoretical understanding of how a deep neural network (DNN) extracts features from input images is still unclear, but it is widely believed that the extraction is performed hierarchically through a process of coarse graining. It reminds us of the basic renormalization group (RG) concept in statistical physics. In order to explore possible relations between DNN and RG, we use the restricted Boltzmann machine (RBM) applied to an Ising model and construct a flow of model parameters (in particular, temperature) generated by the RBM. We show that the unsupervised RBM trained by spin configurations at various temperatures from T =0 to T =6 generates a flow along which the temperature approaches the critical value Tc=2.2 7 . This behavior is the opposite of the typical RG flow of the Ising model. By analyzing various properties of the weight matrices of the trained RBM, we discuss why it flows towards Tc and how the RBM learns to extract features of spin configurations.
Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization group
Dutta, Ayan; Das, Debapriya; Banerjee, Dhruba; Bhattacharjee, Jayanta K.
2018-04-01
While the plausibility of formation of limit cycle has been a well studied topic in context of the Poincare-Bendixson theorem, studies on estimates in regard to the possible size and shape of the limit cycle seem to be scanty in the literature. In this paper we present a pedagogical study of some aspects of the size of this limit cycle using perturbative renormalization group by doing detailed and explicit calculations upto second order for the Selkov model for glycolytic oscillations. This famous model is well known to lead to a limit cycle for certain ranges of values of the parameters involved in the problem. Within the tenets of the approximations made, reasonable agreement with the numerical plots can be achieved.
Real-space renormalization group; application to site percolation in square lattice
International Nuclear Information System (INIS)
Tsallis, C.; Schwachheim, G.
1978-05-01
The real-space renormalization group proposed by Reynolds, Klein and Stanley 1977 to treat the site percolation is analysed and extended . The best among 3 possible definitions of 'percolating' configurations and among 5 possible methods to weight these configurations, are established for percolation in square lattices. The use of n xn square clusters leads, for n = 2 (RKS), n = 3 and n = 4, to √ sub (p) approximately equal to 1.635, √ sub(p) approximately equal to 1.533 and √ sub(p) approximately equal to 1.498, and also to P sub(c) approximately equal to 0.382, P sub(c) approximately equal to 0.388 and P sub(c) approximately equal to 0.398, exhibiting in this way the correct (but slow) tendency towards the best up to date values [pt
Ground states of linear rotor chains via the density matrix renormalization group
Iouchtchenko, Dmitri; Roy, Pierre-Nicholas
2018-04-01
In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.
Fisher's Zeros as the Boundary of Renormalization Group Flows in Complex Coupling Spaces
International Nuclear Information System (INIS)
Denbleyker, A.; Du Daping; Liu Yuzhi; Meurice, Y.; Zou Haiyuan
2010-01-01
We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that Fisher's zeros are located at the boundary of the complex basin of attraction of infrared fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of four-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action stabilize at a distance larger than 0.15 from the real axis in the complex β=4/g 2 plane. We discuss the implications for proofs of confinement and searches for nontrivial infrared fixed points in models beyond the standard model.
Energy Technology Data Exchange (ETDEWEB)
Ansel' m, A A; D' yakonov, D I [AN SSSR, Leningrad. Inst. Yadernoj Fiziki
1975-01-01
The mechanism of dynamic spontaneous breaking of the Coleman-Weinberg gauge invariance is discussed in which scalar fields assume nonzero mean values owing to quantum effects in higher orders of the perturbation theory. Group renormalization methods are used to study scalar electrodynamics and gauge theories similar to that of Yang and Mills; for these gauge theories it is established that by choosing proper constants it is possible to combine the acquisition of a mass by particles, owing to a dynamic violation of symmetry, with the asymptotic freedom of the theory. The symmetry violation is found to be closely related to infrared poles observed in effective charge for asymptotically free theories. The emerging masses of particles automatically cover these poles. It is proved that physical results due to symmetry violation do not depend, at least in the first non-trivial order of the perturbation theory, on the initial gauging of vector fields.
International Nuclear Information System (INIS)
Luo, Da-Wei; Xu, Jing-Bo
2015-01-01
We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs
Semicontinuity of 4d N=2 spectrum under renormalization group flow
International Nuclear Information System (INIS)
Xie, Dan; Yau, Shing-Tung
2016-01-01
We study renormalization group flow of four dimensional N=2 SCFTs defined by isolated hypersurface three-fold singularities. We define the spectrum of N=2 theory as the set of scaling dimensions of the parameters on the Coulomb branch, which include Coulomb branch moduli, mass parameters and coupling constants. We prove that the spectrum of those theories is semicontinous under the RG flow on the Coulomb branch using the mathematical result about the singularity spectra under deformation. The semicontinuity behavior of N=2 spectrum implies a theorem under relevant and Coulomb branch moduli deformation, the absence of dangerous irrelevant deformations and can be taken as the necessary condition for the ending point of a RG flow. This behavior is also true for (c,c) ring deformation of two dimensional Landau-Ginzburg model with (2,2) supersymmetry.
Comparison of renormalization group schemes for sine-Gordon-type models
International Nuclear Information System (INIS)
Nandori, I.; Nagy, S.; Sailer, K.; Trombettoni, A.
2009-01-01
The scheme dependence of the renormalization group (RG) flow has been investigated in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoretic models discussing the applicability of various functional RG methods in detail. It was shown that scheme-independent determination of such physical parameters is possible as the critical frequency (temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition takes place in the sine-Gordon and the layered sine-Gordon models, and the critical ratio characterizing the Ising-type phase transition of the massive sine-Gordon model. For the latter case, the Maxwell construction represents a strong constraint on the RG flow, which results in a scheme-independent infrared value for the critical ratio. For the massive sine-Gordon model also the shrinking of the domain of the phase with spontaneously broken periodicity is shown to take place due to the quantum fluctuations.
Radiative corrections to e+e- reactions to all orders in α using the renormalization group
International Nuclear Information System (INIS)
Tsai, Y.S.
1983-01-01
Renormalization group technique is used to improve the accuracy of the lowest order radiative corrections in QED. The exponentiation of infrared terms comes automatically. It also leads to exponentiation of the vertex functions. It predicts the existence of conversion of photons into pairs and the result agrees with the Kroll-Wada relation. Kinoshita-Lee-Nauenberg cancellation of mass singularities occurs to all order in α in leading log approximation in the final state if we sum over all the final states. Higher order corrections to the order α 3 asymmetry is shown to be small. The results are used to derive useful formulas for the radiative corrections to processes such as e + e - → μ + μ - , e + e - → μ + μ - γ, e + e - → hadron continuum, e + e - → very narrow resonance such as phi, and e + e - → not very narrow resonance such as Z 0
de Sousa, J. Ricardo; de Albuquerque, Douglas F.
1997-02-01
By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one ( N‧ = 1) and two ( N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and ε-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.
Heisenberg spin-one chain in staggered magnetic field: A density matrix renormalization group study
International Nuclear Information System (INIS)
Jizhong Lou; Xi Dai; Shaojin Qin; Zhaobin Su; Lu Yu
1999-04-01
Using the density matrix renormalization group technique, we calculate numerically the low energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of R 2 BaNiO 5 (R ≠ Y) family below the Neel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the non-linear σ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization. (author)
Renormalization group structure for sums of variables generated by incipiently chaotic maps
International Nuclear Information System (INIS)
Fuentes, Miguel Angel; Robledo, Alberto
2010-01-01
We look at the limit distributions of sums of deterministic chaotic variables in unimodal maps and find a remarkable renormalization group (RG) structure associated with the operation of increment of summands and rescaling. In this structure—where the only relevant variable is the difference in control parameter from its value at the transition to chaos—the trivial fixed point is the Gaussian distribution and a novel nontrivial fixed point is a multifractal distribution that emulates the Feigenbaum attractor, and is universal in the sense of the latter. The crossover between the two fixed points is explained and the flow toward the trivial fixed point is seen to be comparable to the chaotic band merging sequence. We discuss the nature of the central limit theorem for deterministic variables
Renormalization group functions of the φ4 theory in the strong coupling limit: Analytical results
International Nuclear Information System (INIS)
Suslov, I. M.
2008-01-01
The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the φ 4 theory by summing perturbation series give the asymptotic behavior β(g) = β ∞ g in the limit g → ∞, where α = 1 for the space dimensions d = 2, 3, 4. It can be hypothesized that the asymptotic behavior is β(g) ∼ g for all d values. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with vanishing of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g) ∼ g in the general d-dimensional case. The asymptotic behaviors of other renormalization group functions are constant. The connection with the zero-charge problem and triviality of the φ 4 theory is discussed
International Nuclear Information System (INIS)
Magalhaes, A.C.N. de; Tsallis, C.; Schwaccheim, G.
1980-04-01
The uncorrelated bond percolation problem is studied in three planar systems where there are two distinct occupancy probabilities. Two different real space renormalization group approaches (referred as the 'canonical' (CRG) and the 'parametric' (PRG) ones) are applied to the anisotropic first-neighbour square lattice, and both of them exhibit the expected tendency towards the exactly known phase boundary (p+q=1). Then, within the context of PRG calculations for increasingly large cells, an extrapolation method is introduced, which leads to analytic proposals for the other two lattices, namely p+q = 1/2 for the first-and second-neighbour square lattice (p and q are, respectively, the first and second neighbour occupancy probabilities), and 3 (p-1/2) = 4 [(1-q) 2 + (1-q) 3 ] (p and q are, respectively, the occupancy probabilities of the topologically different bonds which are in a 1:2 ratio) for the 4- 8 lattice. (Author) [pt
Energy Technology Data Exchange (ETDEWEB)
Tornow, Sabine [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany); Tong, Ning-Hua [Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, 76128 Karlsruhe (Germany); Bulla, Ralf [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg, 86135 Augsburg (Germany)
2006-07-05
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Tornow, Sabine; Tong, Ning-Hua; Bulla, Ralf
2006-07-05
We present a detailed model study of exciton transfer processes in donor-bridge-acceptor (DBA) systems. Using a model which includes the intermolecular Coulomb interaction and the coupling to a dissipative environment we calculate the phase diagram, the absorption spectrum as well as dynamic equilibrium properties with the numerical renormalization group. This method is non-perturbative and therefore allows one to cover the full parameter space, especially the case when the intermolecular Coulomb interaction is of the same order as the coupling to the environment and perturbation theory cannot be applied. For DBA systems with up to six sites we found a transition to the localized phase (self-trapping) depending on the coupling to the dissipative environment. We discuss various criteria which favour delocalized exciton transfer.
Melting the diquark condensate in two-color QCD: A renormalization group analysis
International Nuclear Information System (INIS)
Wirstam, J.; Lenaghan, J.T.; Splittorff, K.
2003-01-01
We use a Landau theory and the ε expansion to study the superfluid phase transition of two-color QCD at a nonzero temperature T and baryonic chemical potential μ. At low T, and for N f flavors of massless quarks, the global SU(N f )xSU(N f )xU(1) symmetry is spontaneously broken by a diquark condensate down to Sp(N f )xSp(N f ) for any μ>0. As the temperature increases, the diquark condensate melts, and at sufficiently large T the symmetry is restored. Using renormalization group arguments, we find that in the presence of the chiral anomaly term there can be a second order phase transition when N f =2 or N f ≥6, while the transition is first order for N f =4. We discuss the relevance of these results for the emergence of a tricritical point recently observed in lattice simulations
From here to criticality: Renormalization group flow between two conformal field theories
International Nuclear Information System (INIS)
Leaf-Herrmann, W.A.
1993-01-01
Using non-perturbative techniques, we study the renormalization group trajectory between two conformal field theories. Specifically, we investigate a perturbation of the A 3 superconformal minimal model such that in the infrared limit the theory flows to the A 2 model. The correlation functions in the topological sector of the theory are computed numerically along the trajectory, and these results are compared to the expected asymptotic behavior. Excellent agreement is found, and the characteristic features of the infrared theory, including the central charge and the normalized operator product expansion coefficients, are obtained. We also review and discuss some aspects of the geometrical description of N=2 supersymmetric quantum field theories recently uncovered by Cecotti and Vafa. (orig.)
Functional renormalization group approach to the Yang-Lee edge singularity
Energy Technology Data Exchange (ETDEWEB)
An, X. [Department of Physics, University of Illinois at Chicago,845 W. Taylor St., Chicago, IL 60607 (United States); Mesterházy, D. [Albert Einstein Center for Fundamental Physics, University of Bern,Sidlerstrasse 5, 3012 Bern (Switzerland); Stephanov, M.A. [Department of Physics, University of Illinois at Chicago,845 W. Taylor St., Chicago, IL 60607 (United States)
2016-07-08
We determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3≤d≤6 Euclidean dimensions. We find very good agreement with high-temperature series data in d=3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ=6−d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂{sup 4}) truncations of the scale-dependent effective action.
Sigma models and renormalization of string loops
International Nuclear Information System (INIS)
Tseytlin, A.A.
1989-05-01
An extension of the ''σ-model β-functions - string equations of motion'' correspondence to the string loop level is discussed. Special emphasis is made on how the renormalization group acts in string loops and, in particular, on the renormalizability property of the generating functional Z-circumflex for string amplitudes (related to the σ model partition function integrated over moduli). Renormalization of Z-circumflex at one and two loop order is analyzed in some detail. We also discuss an approach to renormalization based on operators of insertion of topological fixtures. (author). 70 refs
Renormalization group-theoretic approach to electron localization in disordered systems
International Nuclear Information System (INIS)
Kumar, N.; Heinrichs, J.
1977-06-01
The localization problem for the Anderson tight-binding model with site-diagonal (gaussian) disorder is studied, using a previously established analogy between this problem and the statistical mechanics of a zero-component classical field. The equivalent free-energy functional turns out to have complex coefficients in the bilinear terms but involves a real repulsive quartic interaction. The averaged one-electron propagator corresponds to the two-point correlation function for the equivalent statistical problem and the critical point gives the mobility edge, which is identified with the (real) fixed point energy of the associated renormalization group. Since for convergence reasons the conventional perturbative treatment of Wilson's formula is invalid, it is resorted to a non-perturbative approach which leads to a physical fixed point corresponding to a repulsive quartic interaction. The results for the mobility edge in three dimensions and for the critical disorder for an Anderson transition in two dimensions agree well with previous detailed predictions. The critical indices describing the approach of the transition at the mobility edge of various physical quantities, within the epsilon-expansion are also discussed. The more general problem where both diagonal and off-diagonal disorder is present in the Anderson hamiltonian is considered. In this case it is shown that the Hamilton function for the equivalent zero-component classical field model involves an additional biquadratic exchange term. From a simple generalization of Wilson's recursion relation and its non-perturbative solution explicit expressions for the mobility edges for weak diagonal and off-diagonal disorder in two and three dimensions are obtained. Our treatment casts doubts on the validity of recent conclusions about electron localization based on the renormalization group study of the nm-component spin model
International Nuclear Information System (INIS)
Rodrigues, Davi C.; Oliveira, Paulo L.C. de; Fabris, Julio C.; Shapiro, Ilya L.
2011-01-01
Full text: The running of coupling constants is a well known phenomenon within Quantum Field Theory. It is also known that the renormalization group method can be extended to quantum field theory on curved space time. Nonetheless, although we know that the beta function of QED go to zero in the infrared limit fast enough to lead to constant charge at the classical level (in conformity with both the Appelquist-Carazzone theorem and experimental data), no analogous proof exists for General Relativity. Some authors have proposed that the infrared beta function of General Relativity is not trivial, and as such certain small running of the gravitational coupling might take place at astrophysical scales, leading in particular to changes on the role of dark matter in galaxies. We review and extend our contribution to infrared Renormalization Group (RG) effects to General Relativity in the context of galaxies, an approach we call RGGR. We extend our previous results by analyzing a larger sample of galaxies, now also including elliptical and dwarf spheroidal galaxies, besides disk galaxies (both LSB and HSB). We compare our RGGR results to both standard dark matter profiles (NFW, Isothermal, Burkert) and alternative models of gravity (MOND, MSTG), showing that the RGGR results are similar in quality to the best dark matter profiles (the cored ones, e.g., Isothermal and Burkert), while displaying a better fitting to the data than NFW, MOND or MSTG. To the latter, we evaluated both the shape of the rotation curve and the expected stellar mass-to-light ratios. Dwarf spheroidal (dSph) galaxies are small galaxies believed to be dominated by dark matter, with the highest fraction do dark matter per baryonic matter. These galaxies provide a strong test to any theory that mimics either all or part of the dark matter behavior. In particular, this is the only type of galaxy that MOND seems incapable of fitting the data. (author)
Numerical renormalization group studies of the partially brogen SU(3) Kondo model
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Fuh Chuo, Evaristus
2013-04-15
The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy {Delta}{sub 0}. When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T{sub K}
Numerical renormalization group studies of the partially brogen SU(3) Kondo model
International Nuclear Information System (INIS)
Fuh Chuo, Evaristus
2013-04-01
The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy Δ 0 . When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T K 0 )=k B ln 2 between the high-T value, S(T>>Δ 0 )=k B ln 3, and the 2CK ground state value, S(0)=k B ln √(2). This indicates a downward renormalization of the doublet below the non-interacting ground state, thus realizing the 2CK fixed point, in agreement with earlier conjectures. We mapped out the phase diagram of the model in the J-Δ 0 plane. The Kondo temperature T K shows non-monotonic J-dependence, characteristic for 2CK systems. Beside the two-channel Kondo effect of the model, we also study the single-channel version, which is realized by applying a strong magnetic fi eld to the conduction band electrons so that their degeneracy is lifted and consequently having only one kind of electrons scattering off the impurity. This single-channel case is easier to analyze since the Hilbert space is not as large as that of the 2CK. We equally find a downward renormalization of the excited state energy by the Kondo correlations in the SU(2) doublet. In a wide range of parameter values this stabilizes the single
Dimensional regularization and renormalization of Coulomb gauge quantum electrodynamics
International Nuclear Information System (INIS)
Heckathorn, D.
1979-01-01
Quantum electrodynamics is renormalized in the Coulomb gauge with covariant counter terms and without momentum-dependent wave-function renormalization constants. It is shown how to dimensionally regularize non-covariant integrals occurring in this guage, and prove that the 'minimal' subtraction prescription excludes non-covariant counter terms. Motivated by the need for a renormalized Coulomb gauge formalism in certain practical calculations, the author introduces a convenient prescription with physical parameters. The renormalization group equations for the Coulomb gauge are derived. (Auth.)
Kishine, Jun-ichiro; Yonemitsu, Kenji
1997-01-01
Physical nature of dimensional crossovers in weakly coupled Hubbard chains and ladders has been discussed within the framework of the perturbative renormalization-group approach. The difference between these two cases originates from different universality classes which the corresponding isolated systems belong to.
Algebraic renormalization. Perturbative renormalization, symmetries and anomalies
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Piguet, O.
1995-01-01
This book is an introduction to the algebraic method in the perturbative renormalization of relativistic quantum field theory. After a general introduction to renormalized perturbation theory the quantum action principle and Ward identities are described. Then Yang-Mills gauge theories are considered. Thereafter the BRS cohomology and descent equations are described. Then nonrenormalization theorems and topological field theories are considered. Finally an application to the bosonic string is described. (HSI)
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Cleaver, G.; Cvetic, M.; Everett, L.; Langacker, P.; Wang, J.; Espinosa, J.R.; Everett, L.
1999-01-01
We continue the investigation of the physics implications of a class of flat directions for a prototype quasi-realistic free fermionic string model (CHL5), building upon the results of a previous paper in which the complete mass spectrum and effective trilinear couplings of the observable sector were calculated to all orders in the superpotential. We introduce soft supersymmetry breaking mass parameters into the model, and investigate the gauge symmetry breaking patterns and the renormalization group analysis for two representative flat directions, which leave an additional U(1) ' as well as the SM gauge group unbroken at the string scale. We study symmetry breaking patterns that lead to a phenomenologically acceptable Z-Z ' hierarchy, M Z ' ∼O(1 TeV) and 10 12 GeV for electroweak and intermediate scale U(1) ' symmetry breaking, respectively, and the associated mass spectra after electroweak symmetry breaking. The fermion mass spectrum exhibits unrealistic features, including massless exotic fermions, but has an interesting d-quark hierarchy and associated CKM matrix in one case. There are (some) non-canonical effective μ terms, which lead to a non-minimal Higgs sector with more than two Higgs doublets involved in the symmetry breaking, and a rich structure of Higgs particles, charginos, and neutralinos, some of which, however, are massless or ultralight. In the electroweak scale cases the scale of supersymmetry breaking is set by the Z ' mass, with the sparticle masses in the several TeV range. copyright 1999 The American Physical Society
Will-Nordtvedt PPN formalism applied to renormalization group extensions of general relativity
Toniato, Júnior D.; Rodrigues, Davi C.; de Almeida, Álefe O. F.; Bertini, Nicolas
2017-09-01
We apply the full Will-Nordtvedt version of the parametrized post-Newtonian (PPN) formalism to a class of general relativity extensions that are based on nontrivial renormalization group (RG) effects at large scales. We focus on a class of models in which the gravitational coupling constant G is correlated with the Newtonian potential. A previous PPN analysis considered a specific realization of the RG effects, and only within the Eddington-Robertson-Schiff version of the PPN formalism, which is a less complete and robust PPN formulation. Here we find stronger, more precise bounds, and with less assumptions. We also consider the external potential effect (EPE), which is an effect that is intrinsic to this framework and depends on the system environment (it has some qualitative similarities to the screening mechanisms of modified gravity theories). We find a single particular RG realization that is not affected by the EPE. Some physical systems have been pointed out as candidates for measuring the possible RG effects in gravity at large scales; for any of them the Solar System bounds need to be considered.
Renormalization group scale-setting from the action—a road to modified gravity theories
International Nuclear Information System (INIS)
Domazet, Silvije; Štefančić, Hrvoje
2012-01-01
The renormalization group (RG) corrected gravitational action in Einstein–Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein–Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein–Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor. (paper)
Renormalization group scale-setting from the action—a road to modified gravity theories
Domazet, Silvije; Štefančić, Hrvoje
2012-12-01
The renormalization group (RG) corrected gravitational action in Einstein-Hilbert and other truncations is considered. The running scale of the RG is treated as a scalar field at the level of the action and determined in a scale-setting procedure recently introduced by Koch and Ramirez for the Einstein-Hilbert truncation. The scale-setting procedure is elaborated for other truncations of the gravitational action and applied to several phenomenologically interesting cases. It is shown how the logarithmic dependence of the Newton's coupling on the RG scale leads to exponentially suppressed effective cosmological constant and how the scale-setting in particular RG-corrected gravitational theories yields the effective f(R) modified gravity theories with negative powers of the Ricci scalar R. The scale-setting at the level of the action at the non-Gaussian fixed point in Einstein-Hilbert and more general truncations is shown to lead to universal effective action quadratic in the Ricci tensor.
International Nuclear Information System (INIS)
Fano, G.; Ortolani, F.; Ziosi, L.
1997-10-01
The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A,B. A density matrix ρ is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of ρ are neglected. It is conjectured that the decreasing behaviour of the eigenvalues is gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH) N up to N = 34. A Hilbert space of dimension 5. x 10 18 is explored. The ground state energy is 10 -3 eV within the full Cl value in the case N = 18. The DMRG method compares favourably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a comparison is made with the DMRG energy values. Finally, the spin-spin and density-density correlation functions are computed; the results suggest that the antiferromagnetic order of the exact solution does not extend up to large distances but exists locally. No charge density waves are present. (author)
Renormalization-group improved fully differential cross sections for top pair production
International Nuclear Information System (INIS)
Broggio, A.; Papanastasiou, A.S.; Signer, A.; Zuerich Univ.
2014-07-01
We extend approximate next-to-next-to-leading order results for top-pair production to include the semi-leptonic decays of top quarks in the narrow-width approximation. The new hard-scattering kernels are implemented in a fully differential parton-level Monte Carlo that allows for the study of any IR-safe observable constructed from the momenta of the decay products of the top. Our best predictions are given by approximate NNLO corrections in the production matched to a fixed order calculation with NLO corrections in both the production and decay subprocesses. Being fully differential enables us to make comparisons between approximate results derived via different (PIM and 1PI) kinematics for arbitrary distributions. These comparisons reveal that the renormalization-group framework, from which the approximate results are derived, is rather robust in the sense that applying a realistic error estimate allows us to obtain a reliable prediction with a reduced theoretical error for generic observables and analysis cuts.
Chen, Wei
2018-03-01
For D -dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D - or (D +1 ) -dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.
Extending the range of real time density matrix renormalization group simulations
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ 〉 and operators A in the evaluation of 〈A〉ψ(t) = 〈 ψ | A(t) | ψ 〉 . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
A Renormalization-Group Interpretation of the Connection between Criticality and Multifractals
Chang, Tom
2014-05-01
Turbulent fluctuations in space plasmas beget phenomena of dynamic complexity. It is known that dynamic renormalization group (DRG) may be employed to understand the concept of forced and/or self-organized criticality (FSOC), which seems to describe certain scaling features of space plasma turbulence. But, it may be argued that dynamic complexity is not just a phenomenon of criticality. It is therefore of interest to inquire if DRG may be employed to study complexity phenomena that are distinctly more complicated than dynamic criticality. Power law scaling generally comes about when the DRG trajectory is attracted to the vicinity of a fixed point in the phase space of the relevant dynamic plasma parameters. What happens if the trajectory lies within a domain influenced by more than one single fixed point or more generally if the transformation underlying the DRG is fully nonlinear? The global invariants of the group under such situations (if they exist) are generally not power laws. Nevertheless, as we shall argue, it may still be possible to talk about local invariants that are power laws with the nonlinearity of transformation prescribing a specific phenomenon as crossovers. It is with such concept in mind that we may provide a connection between the properties of dynamic criticality and multifractals from the point of view of DRG (T. Chang, Chapter VII, "An Introduction to Space Plasma Complexity", Cambridge University Press, 2014). An example in terms of the concepts of finite-size scaling (FSS) and rank-ordered multifractal analysis (ROMA) of a toy model shall be provided. Research partially supported by the US National Science Foundation and the European Community's Seventh Framework Programme (FP7/ 2007-2013) under Grant agreement no. 313038/STORM.
International Nuclear Information System (INIS)
Lopatnikova, A.; Berker, A.N.
1997-01-01
Superfluidity and phase separation in 3 He- 4 He mixtures immersed in aerogel are studied by renormalization-group theory. The quenched disorder imposed by aerogel, both at the atomic level and at the geometric level, is included. The calculation is conducted via the coupled renormalization-group mappings, near and away from aerogel, of the quenched probability distributions of random interactions. Random-bond effects on the onset of superfluidity and random-field effects on superfluid-superfluid phase separation are seen. The quenched randomness causes the λ line of second-order phase transitions of superfluidity onset to reach zero temperature, in agreement with general predictions and experiments. The effects of the atomic and geometric randomness of aerogel are investigated separately and jointly. copyright 1997 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Keller, G. (Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut); Kopper, C. (Goettingen Univ. (Germany). Inst. fuer Theoretische Physik)
1993-04-01
We give a rigorous and very detailed derivation of the short distance expansion for a product of two arbitrary composite operators in the framework of the perturbative Euclidean massive [Phi][sub 4][sup 4]. The technically almost trivial proof rests on an extension of the differential flow equation method to Green functions with bilocal insertions, for which we also establish a set of generalized Zimmermann identities and Lowenstein rules. (orig.).
Directory of Open Access Journals (Sweden)
Shivani Gupta
2015-04-01
Full Text Available We examine the renormalization group evolution (RGE for different mixing scenarios in the presence of seesaw threshold effects from high energy scale (GUT to the low electroweak (EW scale in the Standard Model (SM and Minimal Supersymmetric Standard Model (MSSM. We consider four mixing scenarios namely Tri–Bimaximal Mixing, Bimaximal Mixing, Hexagonal Mixing and Golden Ratio Mixing which come from different flavor symmetries at the GUT scale. We find that the Majorana phases play an important role in the RGE running of these mixing patterns along with the seesaw threshold corrections. We present a comparative study of the RGE of all these mixing scenarios both with and without Majorana CP phases when seesaw threshold corrections are taken into consideration. We find that in the absence of these Majorana phases both the RGE running and seesaw effects may lead to θ13<5° at low energies both in the SM and MSSM. However, if the Majorana phases are incorporated into the mixing matrix the running can be enhanced both in the SM and MSSM. Even by incorporating non-zero Majorana CP phases in the SM, we do not get θ13 in its present 3σ range. The current values of the two mass squared differences and mixing angles including θ13 can be produced in the MSSM case with tanβ=10 and non-zero Majorana CP phases at low energy. We also calculate the order of effective Majorana mass and Jarlskog Invariant for each scenario under consideration.
International Nuclear Information System (INIS)
Muender, W; Weichselbaum, A; Holzner, A; Delft, Jan von; Henley, C L
2010-01-01
A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix (CDM). For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all the correlations between the two clusters. We show how to extract from the CDM a survey of the relative strengths of the system's correlations in different symmetry sectors and the nature of their decay with distance (power law or exponential), as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To achieve this goal, we introduce a new method of analysing the CDM, termed the dominant operator basis (DOB) method, which identifies in an unbiased fashion a small set of operators for each cluster that serve as a basis for the dominant correlations of the system. We illustrate this method by analysing the CDM for a spinless extended Hubbard model that features a competition between charge density correlations and pairing correlations, and show that the DOB method successfully identifies their relative strengths and dominant correlators. To calculate the ground state of this model, we use the density matrix renormalization group, formulated in terms of a variational matrix product state (MPS) approach within which subsequent determination of the CDM is very straightforward. In an extended appendix, we give a detailed tutorial introduction to our variational MPS approach for ground state calculations for one-dimensional quantum chain models. We present in detail how MPSs overcome the problem of large Hilbert space dimensions in these models and describe all the techniques needed for handling them in practice.
Merker, L.; Costi, T. A.
2012-08-01
We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-28
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
Bischoff, Jan-Moritz; Jeckelmann, Eric
2017-11-01
We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.
Directory of Open Access Journals (Sweden)
V. Bacsó
2015-12-01
Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.
International Nuclear Information System (INIS)
Magalhaes, A.C.N. de.
1982-01-01
By using real space renormalization group methods, bond percolation on d-dimensional hypercubic (d = 2, 3, 4), first - and second - neighbour isotropic square, anisotropic square and 'inhomogeneous' 4-8 lattices is studied. Through some extrapolation methods, critical points and/or frontiers are obtained (as well as the critical exponent ν sub(p) in the isotropic cases) for these lattices that, or agree well with other available results, or are new as far as it is know (first - and second - neighbour isotropic square and 'inhomogeneous' 4-8 lattices). A conjecture concerning approximate (eventually exact) critical points and, in certain situations, critical frontiers of q-state Potts ferromagnets on d-dimensional lattices (d > 1) is formulated. This conjecture is verified within good accuracy for all the lattices whose critical points are known, and it allows the prediction of a great number of new results, some of them it is believed to be exact. Within a real space renomalization group framework, accurate approximations for the critical frontiers associated with the quenched bond-diluted first-neighbour spin-1/2 Ising ferromagnet on triangular and honeycomb lattices are calculated. The best numerical proposals lead, in both pure bond percolation (p = p sub(c)) and pure Ising (p = 1) limits, to the exact critical points and (dt 0 /dp) sub(p = p sub(c)) (where t 0 identical to tanh J/K sub(B) T), and to a 0.15% (0.96%) error in (dt 0 /dp) sub(p = 1) for the triangular (honeycomb) lattice; for p sub(c) 0 (for fixed p) of 0.27% (0.14%) is estimated for the triangular (honeycomb) lattice. It is exhibited, for many star-triangle graph pairs with any number of terminals and different sizes, that the exact q = 1, 2, 3, 4 critical points of Potts ferromagnets can aZZ of them, be obtained from any one of such graph pairs. (Author) [pt
A comprehensive coordinate space renormalization of quantum electrodynamics to two-loop order
International Nuclear Information System (INIS)
Haagensen, P.E.; Latorre, J.I.
1993-01-01
We develop a coordinate space renormalization of massless quantum electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all one- and two-loop 1PI diagrams, run renormalization group equations on them. and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle γ 5 problems
International Nuclear Information System (INIS)
Platt, Christian
2012-01-01
The superconducting properties of complex materials like the recently discovered iron-pnictides or strontium-ruthenate are often governed by multi-orbital effects. In order to unravel the superconductivity of those materials, we develop a multi-orbital implementation of the functional renormalization group and study the pairing states of several characteristic material systems. Starting with the iron-pnictides, we find competing spin-fluctuation channels that become attractive if the superconducting gap changes sign between the nested portions of the Fermi surface. Depending on material details like doping or pnictogen height, these spin fluctuations then give rise to s ± -wave pairing with or without gap nodes and, in some cases, also change the symmetry to d-wave. Near the transition from nodal s ± -wave to d-wave pairing, we predict the occurrence of a time-reversal symmetry-broken (s+id)-pairing state which avoids gap nodes and is therefore energetically favored. We further study the electronic instabilities of doped graphene, another fascinating material which has recently become accessible and which can effectively be regarded as multi-orbital system. Here, the hexagonal lattice structure assures the degeneracy of two d-wave pairing channels, and the system then realizes a chiral (d+id)-pairing state in a wide doping range around van-Hove filling. In addition, we also find spin-triplet pairing as well as an exotic spin-density wave phase which both become leading if the long-ranged hopping or interaction parameters are slightly modified, for example, by choosing different substrate materials. Finally, we consider the superconducting state of strontium-ruthenate, a possible candidate for chiral spin-triplet pairing with fascinating properties like the existence of half-quantum vortices obeying non-Abelian statistics. Using a microscopic three orbital description including spin-orbit coupling, we demonstrate that ferromagnetic fluctuations are still
Renormalization group study of the multi-layer sine-gordon model
International Nuclear Information System (INIS)
Nandori, I.
2005-01-01
Complete text of publication follows. We analyze the phase structure of the system of coupled sine-Gordon (SG) type field theoric models. The 'pure,' SG model is periodic in the internal space spanned by the field variable. The central subjects of investigation is the multi-layer sine-Gordon (LSG) model, where the periodicity is broken partially by the coupling terms between the layers each of which is described by a scalar field, where the second term on the r.h.s. describes the interaction of the layers. Here, we dis- cuss the generalization of the results obtained for the two-layer sine-Gordon model found in the previous study. Besides the obvious field theoretical interest, the LSG model has been used to describe the vortex properties of high transition temperature superconductors, and the extension of the previous analysis to a general N-layer model is necessary for a description of the critical behaviour of vortices in realistic multi-layer systems. The couplings between the layers can be considered as mass terms. Since the periodicity of the LSG model has been broken only partially, the N-layer model has always a single zero mass eigenvalue. The presence of this single zero mass eigenvalue is found to be decisive with respect to the phase structure of the N-layer models. By a suitable rotation of the field variables, we identify the periodic mode (which corresponds to the zero mass eigenvalue) and N - 1 non-periodic modes (with explicit mass terms). The N - 1 non-periodic modes have a trivial IR scaling which holds independently of β which has been proven consistently using (i) the non-perturbative renormalization group study of the rotated model, (ii) the Gaussian integration about the vanishing-field saddle point. Due to the presence of the periodic mode the model undergoes a Kosterlitz-Thouless type phase transition which occurs at a coupling parameter β c 2 = 8Nπ, where N is the number of layers. The critical value β c 2 corresponds to the critical
Construction of Difference Equations Using Lie Groups
International Nuclear Information System (INIS)
Axford, R.A.
1998-01-01
The theory of prolongations of the generators of groups of point transformations to the grid point values of dependent variables and grid spacings is developed and applied to the construction of group invariant numerical algorithms. The concepts of invariant difference operators and generalized discrete sources are introduced for the discretization of systems of inhomogeneous differential equations and shown to produce exact difference equations. Invariant numerical flux functions are constructed from the general solutions of first order partial differential equations that come out of the evaluation of the Lie derivatives of conservation forms of difference schemes. It is demonstrated that invariant numerical flux functions with invariant flux or slope limiters can be determined to yield high resolution difference schemes. The introduction of an invariant flux or slope limiter can be done so as not to break the symmetry properties of a numerical flux-function
International Nuclear Information System (INIS)
Snowman, Daniel P.
2009-01-01
Phase diagrams have been produced and critical exponents calculated for a Blume-Emery-Griffiths system with competing biquadratic and crystal-field interactions with uniform ferromagnetic bilinear interactions. This competition directly effects the clustering and density of nonmagnetic impurities. These results have been produced using renormalization-group methods with a hierarchical lattice. A series of planes of constant, repulsive biquadratic coupling have been probed while varying the temperature and concentration of annealed vacancies in the system. The sinks have been analyzed and interpreted, and critical exponents calculated for the higher order transitions.
Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic
2018-05-01
We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.
International Nuclear Information System (INIS)
Honda, Yasushi; Horiguchi, Tsuyoshi
2001-01-01
We investigate a uniformly frustrated 19-vertex model with an anisotropy parameter η by use of the density matrix renormalization group for the transfer matrix for 0.6≤η≤1.3. The scaling dimension x is calculated from eigenvalues of the transfer matrix for several values η. The finite-size scaling analyses with a logarithmic correction are carried out in order to determine transition temperatures. It is found that there are two kinds of phase transitions, although there is a possibility of a single transition. This result is not compatible with the result for the uniformly frustrated XY model
International Nuclear Information System (INIS)
Mikhailov, I.D.; Zhuravskii, L.V.
1987-01-01
A method is proposed for calculating the vibrational-state density averaged over all configurations for a polymer chain with Markov disorder. The method is based on using a group of centrally symmetric gauge transformations that reduce the dynamic matrix for along polymer chain to renormalized dynamic matrices for short fragments. The short-range order is incorporated exactly in the averaging procedure, while the long-range order is incorporated in the self-consistent field approximation. Results are given for a simple skeletal model for a polymer containing tacticity deviations of Markov type
Energy Technology Data Exchange (ETDEWEB)
Foster, D P; Pinettes, C [Laboratoire de Physique Theorique et Modelisation (CNRS UMR 8089), Universite de Cergy-Pontoise, 5 Mail Gay-Lussac 95031, Cergy-Pontoise Cedex (France)
2003-10-17
A recently introduced extension of the corner transfer matrix renormalization group method useful for the study of self-avoiding walk-type models is presented in detail and applied to a class of interacting self-avoiding walks due to Bloete and Nienhuis. This model displays two different types of collapse transition depending on model parameters. One is the standard {theta}-point transition. The other is found to give rise to a first-order collapse transition despite being known to be in other respects critical.
Field renormalization in photonic crystal waveguides
DEFF Research Database (Denmark)
Colman, Pierre
2015-01-01
A novel strategy is introduced in order to include variations of the nonlinearity in the nonlinear Schro¨dinger equation. This technique, which relies on renormalization, is in particular well adapted to nanostructured optical systems where the nonlinearity exhibits large variations up to two...... orders of magnitude larger than in bulk material. We show that it takes into account in a simple and efficient way the specificity of the nonlinearity in nanostructures that is determined by geometrical parameters like the effective mode area and the group index. The renormalization of the nonlinear...
Alonso, Rodrigo; Manohar, Aneesh V; Trott, Michael
2014-01-01
We calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the $\\lambda$ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 $CP$-even and $1149$ $CP$-odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire $2499 \\times 2499$ anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension $d \\le 4$ terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as $gg \\to h...
Solution of differential equations by application of transformation groups
Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.
1968-01-01
Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.
Renormalization and plasma physics
International Nuclear Information System (INIS)
Krommes, J.A.
1980-02-01
A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields
Renormalization and plasma physics
Energy Technology Data Exchange (ETDEWEB)
Krommes, J.A.
1980-02-01
A review is given of modern theories of statistical dynamics as applied to problems in plasma physics. The derivation of consistent renormalized kinetic equations is discussed, first heuristically, later in terms of powerful functional techniques. The equations are illustrated with models of various degrees of idealization, including the exactly soluble stochastic oscillator, a prototype for several important applications. The direct-interaction approximation is described in detail. Applications discussed include test particle diffusion and the justification of quasilinear theory, convective cells, E vector x B vector turbulence, the renormalized dielectric function, phase space granulation, and stochastic magnetic fields.
Roberts, Brenden; Vidick, Thomas; Motrunich, Olexei I.
2017-12-01
The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017), 10.1007/s00220-017-2973-z]. The convergence proof, however, relies on "rigorous renormalization group" (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.
Heyl, Markus; Vojta, Matthias
2015-09-01
In this work we formulate the nonequilibrium dynamical renormalization group (ndRG). The ndRG represents a general renormalization-group scheme for the analytical description of the real-time dynamics of complex quantum many-body systems. In particular, the ndRG incorporates time as an additional scale which turns out to be important for the description of the long-time dynamics. It can be applied to both translational-invariant and disordered systems. As a concrete application, we study the real-time dynamics after a quench between two quantum critical points of different universality classes. We achieve this by switching on weak disorder in a one-dimensional transverse-field Ising model initially prepared at its clean quantum critical point. By comparing to numerically exact simulations for large systems, we show that the ndRG is capable of analytically capturing the full crossover from weak to infinite randomness. We analytically study signatures of localization in both real space and Fock space.
Renormalization and effective actions for general relativity
International Nuclear Information System (INIS)
Neugebohrn, F.
2007-05-01
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)
Renormalization and effective actions for general relativity
Energy Technology Data Exchange (ETDEWEB)
Neugebohrn, F.
2007-05-15
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at scales far below the UV cutoff. In particular, nonrenormalizable theories can be treated without problems in the proposed framework. In the second part, the standard covariant BRS quantization program for Euclidean Einstein gravity is applied. A momentum cutoff regularization is imposed and the resulting violation of the Slavnov-Taylor identities is discussed. Deriving Polchinski's renormalization group equation for Euclidean quantum gravity, the predictivity of effective quantum gravity at scales far below the Planck scale is investigated with flow equations. A fine-tuning procedure for restoring the violated Slavnov-Taylor identities is proposed and it is argued that in the effective quantum gravity context, the restoration will only be accomplished with finite accuracy. Finally, the no-cutoff limit of Euclidean quantum gravity is analyzed from the viewpoint of the Polchinski method. It is speculated whether a limit with nonvanishing gravitational constant might exist where the latter would ultimatively be determined by the cosmological constant and the masses of the elementary particles. (orig.)
International Nuclear Information System (INIS)
Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua
2015-01-01
We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)
International Nuclear Information System (INIS)
Pivovarov, A.A.
2003-01-01
The analytic structure in the strong coupling constant that emerges for some observables in QCD after duality averaging of renormalization-group-improved amplitudes is discussed, and the validity of the infrared renormalon hypothesis for the determination of this structure is critically reexamined. A consistent description of peculiar features of perturbation theory series related to hypothetical infrared renormalons and corresponding power corrections is considered. It is shown that perturbation theory series for the spectral moments of two-point correlators of hadronic currents in QCD can explicitly be summed in all orders using the definition of the moments that avoids integration through the infrared region in momentum space. Such a definition of the moments relies on the analytic properties of two-point correlators in the momentum variable that allows for shifting the integration contour into the complex plane of the momentum. For definiteness, an explicit case of gluonic current correlators is discussed in detail
International Nuclear Information System (INIS)
Martin, H.O.; Tsallis, C.
1981-01-01
A simple renormalization group approach based on self-dual clusters is proposed for two-dimensional nearest-neighbour 1/2 - spin Ising model on the square lattice; it reproduces the exact critical point. The internal energy and the specific heat for vanishing external magnetic field, spontaneous magnetization and the thermal (Y sub(T)) and magnetic (Y sub(H)) critical exponents are calculated. The results obtained from the first four smallest cluster sizes strongly suggest the convergence towards the exact values when the cluster sizes increases. Even for the smallest cluster, where the calculation is very simple, the results are quite accurate, particularly in the neighbourhood of the critical point. (Author) [pt
Application of the algebraic RNG model for transition simulation. [renormalization group theory
Lund, Thomas S.
1990-01-01
The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.
Long, Feng-Shan; Karnbanjong, Adisak; Suriyawichitseranee, Amornrat; Grigoriev, Yurii N.; Meleshko, Sergey V.
2017-07-01
This paper proposes an algorithm for group classification of a nonhomogeneous equation using the group analysis provided for the corresponding homogeneous equation. The approach is illustrated by a partial differential equation, an integro-differential equation, and a delay partial differential equation.
Kumar, Manoranjan
2016-02-03
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.
Kumar, Manoranjan; Parvej, Aslam; Thomas, Simil; Ramasesha, S.; Soos, Z. G.
2016-01-01
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.
On the effect of renormalization group improvement on the cosmological power spectrum
Energy Technology Data Exchange (ETDEWEB)
Moti, R. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Shojai, A. [University of Tehran, Department of Physics, Tehran (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), Foundations of Physics Group, School of Physics, Tehran (Iran, Islamic Republic of)
2018-01-15
Asymptotically safe quantum gravity predicts running gravitational and cosmological constants, while it remains a meaningful quantum field theory because of the existence of a finite number of non-Gaussian ultraviolet fixed points. We have investigated the effect of such running couplings on the cosmological perturbations. We have obtained the improved Mukhanov-Sassaki equation and solved it for two models. The effect of such running of the coupling constants on the cosmological power spectrum is also studied. (orig.)
Forte, Esther; Llovell, Felix; Vega, Lourdes F; Trusler, J P Martin; Galindo, Amparo
2011-04-21
An accurate prediction of phase behavior at conditions far and close to criticality cannot be accomplished by mean-field based theories that do not incorporate long-range density fluctuations. A treatment based on renormalization-group (RG) theory as developed by White and co-workers has proven to be very successful in improving the predictions of the critical region with different equations of state. The basis of the method is an iterative procedure to account for contributions to the free energy of density fluctuations of increasing wavelengths. The RG method has been combined with a number of versions of the statistical associating fluid theory (SAFT), by implementing White's earliest ideas with the improvements of Prausnitz and co-workers. Typically, this treatment involves two adjustable parameters: a cutoff wavelength L for density fluctuations and an average gradient of the wavelet function Φ. In this work, the SAFT-VR (variable range) equation of state is extended with a similar crossover treatment which, however, follows closely the most recent improvements introduced by White. The interpretation of White's latter developments allows us to establish a straightforward method which enables Φ to be evaluated; only the cutoff wavelength L then needs to be adjusted. The approach used here begins with an initial free energy incorporating only contributions from short-wavelength fluctuations, which are treated locally. The contribution from long-wavelength fluctuations is incorporated through an iterative procedure based on attractive interactions which incorporate the structure of the fluid following the ideas of perturbation theories and using a mapping that allows integration of the radial distribution function. Good agreement close and far from the critical region is obtained using a unique fitted parameter L that can be easily related to the range of the potential. In this way the thermodynamic properties of a square-well (SW) fluid are given by the same
Nataf, Pierre; Mila, Frédéric
2018-04-01
We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.
Jenkins, Elizabeth E; Trott, Michael
2013-01-01
We calculate the order \\lambda, \\lambda^2 and \\lambda y^2 terms of the 59 x 59 one-loop anomalous dimension matrix of dimension-six operators, where \\lambda and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.
International Nuclear Information System (INIS)
Yamada, Susumu; Igarashi, Ryo; Machida, Masahiko; Imamura, Toshiyuki; Okumura, Masahiko; Onishi, Hiroaki
2010-01-01
We parallelize the density matrix renormalization group (DMRG) method, which is a ground-state solver for one-dimensional quantum lattice systems. The parallelization allows us to extend the applicable range of the DMRG to n-leg ladders i.e., quasi two-dimension cases. Such an extension is regarded to bring about several breakthroughs in e.g., quantum-physics, chemistry, and nano-engineering. However, the straightforward parallelization requires all-to-all communications between all processes which are unsuitable for multi-core systems, which is a mainstream of current parallel computers. Therefore, we optimize the all-to-all communications by the following two steps. The first one is the elimination of the communications between all processes by only rearranging data distribution with the communication data amount kept. The second one is the avoidance of the communication conflict by rescheduling the calculation and the communication. We evaluate the performance of the DMRG method on multi-core supercomputers and confirm that our two-steps tuning is quite effective. (author)
Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo
2018-01-18
The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.
Fang, Tie-Feng; Guo, Ai-Min; Sun, Qing-Feng
2018-06-01
We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction U is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing a negative-U charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. 8, 395 (2017), 10.1038/s41467-017-00495-7].
Nosov, P. A.; Kishine, Jun-ichiro; Ovchinnikov, A. S.; Proskurin, I.
2017-12-01
We consider a possibility of the topological Kosterlitz-Thouless (KT) transition in the two-dimensional Pokrovsky-Talapov model with a finite misfit parameter and discuss its relevance to the theory of critical behavior in thin films of monoaxial chiral helimagnets. For this purpose, the initial model is reformulated in terms of the two-dimensional relativistic model of massive Thirring fermions and the Wetterich's functional renormalization-group (RG) approach is employed. In the new formalism, the misfit parameter corresponds to an effective gauge field that can be included in the RG scheme on an equal footing with the other parameters of the theory. Our main result is that the presence of the misfit parameter, which may be attributed to the Dzyaloshinskii-Moriya interaction in the magnetic system, rules out the KT transition. To support this finding, we provide an additional intuitive explanation of the KT scenario breakdown by using the mapping onto the Coulomb gas model. In the framework of the model, the misfit parameter has a meaning of an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.
International Nuclear Information System (INIS)
Kishine, Jun-Ichiro; Yonemitsu, Kenji
1998-01-01
Physical nature of dimensional crossovers in weakly coupled Hubbard chains and ladders has been discussed within the framework of the perturbative renormalization-group (PRG) approach. The difference between these two cases originates from different universality classes which the corresponding isolated systems belong to. In the present work, we discuss the nature of the dimensional crossovers in the weakly coupled chains and ladders, with emphasis on the difference between the two cases within the framework of the PRG approach. The difference of the universality class of the isolated chain and ladder profoundly affects the relevance or irrelevance of the inter-chain/ladder one-particle hopping. The strong coupling phase of the isolated ladder makes the one-particle process irrelevant so that the d-wave superconducting transition can be induced via the two-particle crossover in the weakly coupled ladders. The weak coupling phase of the isolated chain makes the one-particle process relevant so that the two-particle crossover can hardly be realized in the coupled chains. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Constructive renormalization theory
International Nuclear Information System (INIS)
Rivasseau, Vincent
2000-01-01
These notes are the second part of a common course on Renormalization Theory given with Professor P. da Veiga. I emphasize here the rigorous non-perturbative or constructive aspects of the theory. The usual formalism for the renormalization group in field theory or statistical mechanics is reviewed, together with its limits. The constructive formalism is introduced step by step. Taylor forest formulas allow to perform easily the cluster and Mayer expansions which are needed for a single step of the renormalization group in the case of Bosonic theories. The iteration of this single step leads to further difficulties whose solution is briefly sketched. The second part of the course is devoted to Fermionic models. These models are easier to treat on the constructive level so they are very well suited to beginners in constructive theory. It is shown how the Taylor forest formulas allow to reorganize perturbation theory nicely in order to construct the Gross-Neveu 2 model without any need for cluster or Mayer expansions. Finally applications of this technique to condensed matter and renormalization group around Fermi surface are briefly reviewed. (author)
Linear perturbation renormalization group method for Ising-like spin systems
Directory of Open Access Journals (Sweden)
J. Sznajd
2013-03-01
Full Text Available The linear perturbation group transformation (LPRG is used to study the thermodynamics of the axial next-nearest-neighbor Ising model with four spin interactions (extended ANNNI in a field. The LPRG for weakly interacting Ising chains is presented. The method is used to study finite field para-ferrimagnetic phase transitions observed in layered uranium compounds, UAs1-xSex, UPd2Si2 or UNi2Si2. The above-mentioned systems are made of ferromagnetic layers and the spins from the nearest-neighbor and next-nearest-neighbor layers are coupled by the antiferromagnetic interactions J121-xSex the para-ferri phase transition is of the first order as expected from the symmetry reason, in UT2Si2 (T=Pd, Ni this transition seems to be a continuous one, at least in the vicinity of the multicritical point. Within the MFA, the critical character of the finite field para-ferrimagnetic transition at least at one isolated point can be described by the ANNNI model supplemented by an additional, e.g., four-spin interaction. However, in LPRG approximation for the ratio κ = J2/J1 around 0.5 there is a critical value of the field for which an isolated critical point also exists in the original ANNNI model. The positive four-spin interaction shifts the critical point towards higher fields and changes the shape of the specific heat curve. In the latter case for the fields small enough, the specific heat exhibits two-peak structure in the paramagnetic phase.
Garcia-Adeva, A. J.; Huber, D. L.
2001-01-01
In this work we generalize and subsequently apply the Effective Field Renormalization Group technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagome and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As ...
Energy Technology Data Exchange (ETDEWEB)
Roemelt, Michael, E-mail: michael.roemelt@theochem.rub.de [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany and Max-Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
The Analytic Renormalization Group
Ferrari, Frank
2016-01-01
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\\in\\mathbb Z$, associated with the Matsubara frequencies $\
An integral equation arising in two group neutron transport theory
International Nuclear Information System (INIS)
Cassell, J S; Williams, M M R
2003-01-01
An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically
Equivalence groups of (2+1) dimensional diffusion equation
Özer, Saadet
2017-01-01
If a given set of differential equations contain somearbitrary functions, parameters, we have in fact a family of sets of equationsof the same structure. Almost all field equations of classical physichs havethis property, representing different materials with various paramaters. Equivalence groups are defined as the groupof transformations which leave a given family of differential equationsinvariant. Therefore, equivalence group of family of differential equations isan important area within...
Renormalization-scheme-invariant QCD and QED: The method of effective charges
International Nuclear Information System (INIS)
Grunberg, G.
1984-01-01
We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding Stueckelberg--Peterman--Gell-Mann--Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter Λ, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass m is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales
Renormalization scheme-invariant perturbation theory
International Nuclear Information System (INIS)
Dhar, A.
1983-01-01
A complete solution to the problem of the renormalization scheme dependence of perturbative approximants to physical quantities is presented. An equation is derived which determines any physical quantity implicitly as a function of only scheme independent variables. (orig.)
Miao, Jian-Jian; Jin, Hui-Ke; Zhang, Fu-Chun; Zhou, Yi
2018-01-11
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
Renormalization Methods - A Guide For Beginners
International Nuclear Information System (INIS)
Cardy, J
2004-01-01
The stated goal of this book is to fill a perceived gap between undergraduate texts on critical phenomena and advanced texts on quantum field theory, in the general area of renormalization methods. It is debatable whether this gap really exists nowadays, as a number of books have appeared in which it is made clear that field-theoretic renormalization group methods are not the preserve of particle theory, and indeed are far more easily appreciated in the contexts of statistical and condensed matter physics. Nevertheless, this volume does have a fresh aspect to it, perhaps because of the author's background in fluid dynamics and turbulence theory, rather than through the more traditional migration from particle physics. The book begins at a very elementary level, in an effort to motivate the use of renormalization methods. This is a worthy effort, but it is likely that most of this section will be thought too elementary by readers wanting to get their teeth into the subject, while those for whom this section is apparently written are likely to find the later chapters rather challenging. The author's particular approach then leads him to emphasise the role of renormalized perturbation theory (rather than the renormalization group) in a number of problems, including non-linear systems and turbulence. Some of these ideas will be novel and perhaps even surprising to traditionally trained field theorists. Most of the rest of the book is on far more familiar territory: the momentum-space renormalization group, epsilon-expansion, and so on. This is standard stuff, and, like many other textbooks, it takes a considerable chunk of the book to explain all the formalism. As a result, there is only space to discuss the standard φ 4 field theory as applied to the Ising model (even the N-vector model is not covered) so that no impression is conveyed of the power and extent of all the applications and generalizations of the techniques. It is regrettable that so much space is spent
On the monodromy group for the super Schwarzian differential equation
International Nuclear Information System (INIS)
Uehara, Shozo; Yasui, Yukinori.
1991-03-01
We calculate the first variation of the monodromy group associated with a super Schwarzian differential equation. The relation between the monodromy period and the Fenchel-Nielsen deformation of a super Riemann surface is presented. (author)
The renormalization scale-setting problem in QCD
Energy Technology Data Exchange (ETDEWEB)
Wu, Xing-Gang [Chongqing Univ. (China); Brodsky, Stanley J. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Mojaza, Matin [SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Southern Denmark, Odense (Denmark)
2013-09-01
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to fixed-order pQCD predictions. In fact, this ad hoc procedure gives results which depend on the choice of the renormalization scheme, and it is in conflict with the standard scale-setting procedure used in QED. Predictions for physical results should be independent of the choice of the scheme or other theoretical conventions. We review current ideas and points of view on how to deal with the renormalization scale ambiguity and show how to obtain renormalization scheme- and scale-independent estimates. We begin by introducing the renormalization group (RG) equation and an extended version, which expresses the invariance of physical observables under both the renormalization scheme and scale-parameter transformations. The RG equation provides a convenient way for estimating the scheme- and scale-dependence of a physical process. We then discuss self-consistency requirements of the RG equations, such as reflexivity, symmetry, and transitivity, which must be satisfied by a scale-setting method. Four typical scale setting methods suggested in the literature, i.e., the Fastest Apparent Convergence (FAC) criterion, the Principle of Minimum Sensitivity (PMS), the Brodsky–Lepage–Mackenzie method (BLM), and the Principle of Maximum Conformality (PMC), are introduced. Basic properties and their applications are discussed. We pay particular attention to the PMC, which satisfies all of the requirements of RG invariance. Using the PMC, all non-conformal terms associated with the β-function in the perturbative series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC provides the principle underlying the BLM method, since it gives the general rule for extending
Kurashige, Yuki; Yanai, Takeshi
2011-09-07
We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics
Renormalized action improvements
International Nuclear Information System (INIS)
Zachos, C.
1984-01-01
Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references
Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras
Put, Marius van der
1999-01-01
The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.
Lie symmetries and differential galois groups of linear equations
Oudshoorn, W.R.; Put, M. van der
2002-01-01
For a linear ordinary differential equation the Lie algebra of its infinitesimal Lie symmetries is compared with its differential Galois group. For this purpose an algebraic formulation of Lie symmetries is developed. It turns out that there is no direct relation between the two above objects. In
Consequences of Violated Equating Assumptions under the Equivalent Groups Design
Lyren, Per-Erik; Hambleton, Ronald K.
2011-01-01
The equal ability distribution assumption associated with the equivalent groups equating design was investigated in the context of a selection test for admission to higher education. The purpose was to assess the consequences for the test-takers in terms of receiving improperly high or low scores compared to their peers, and to find strong…
Functional renormalization and ultracold quantum gases
International Nuclear Information System (INIS)
Floerchinger, Stefan
2010-01-01
Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics. (orig.)
Sznajd, J.
2016-12-01
The linear perturbation renormalization group (LPRG) is used to study the phase transition of the weakly coupled Ising chains with intrachain (J ) and interchain nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions forming the triangular and rectangular lattices in a field. The phase diagrams with the frustration point at J2=-J1/2 for a rectangular lattice and J2=-J1 for a triangular lattice have been found. The LPRG calculations support the idea that the phase transition is always continuous except for the frustration point and is accompanied by a divergence of the specific heat. For the antiferromagnetic chains, the external field does not change substantially the shape of the phase diagram. The critical temperature is suppressed to zero according to the power law when approaching the frustration point with an exponent dependent on the value of the field.
Energy Technology Data Exchange (ETDEWEB)
Okumura, M; Onishi, H; Yamada, S; Machida, M, E-mail: okumura@riken.j
2010-11-01
We study non-equilibrium properties of one-dimensional Hubbard model by the density-matrix renormalization-group method. First, we demonstrate stability of 'doublon', which characterized by double occupation on a site due to the integrability of the model. Next, we present a kind of anomalous transport caused by the doublons created under strong non-equilibrium conditions in an optical lattice system regarded as an ideal testbed to investigate fundamental properties of the Hubbard model. Finally, we give a result on development of the pair correlation function in a strong non-equilibrium condition. This can be understood as a development of coherence among many excited doublons.
Lectures on the theory of group properties of differential equations
Ovsyannikov, LV
2013-01-01
These lecturers provide a clear introduction to Lie group methods for determining and using symmetries of differential equations, a variety of their applications in gas dynamics and other nonlinear models as well as the author's remarkable contribution to this classical subject. It contains material that is useful for students and teachers but cannot be found in modern texts. For example, the theory of partially invariant solutions developed by Ovsyannikov provides a powerful tool for solving systems of nonlinear differential equations and investigating complicated mathematical models. Readers
Garcia-Adeva, Angel J.; Huber, David L.
2001-07-01
In this work we generalize and subsequently apply the effective-field renormalization-group (EFRG) technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagomé and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin-ice model can be exactly mapped to the standard Ising model, but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated and does not order. Antiferromagnetic spin ice (in both two and three dimensions) is found to undergo a transition to a long-range-ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced generalized constant coupling method is also applied to the calculation of the critical points and ground-state configurations. Again, a very good agreement is found with exact, Monte Carlo, and renormalization-group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest-order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.
Linearized pseudo-Einstein equations on the Heisenberg group
Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard
2017-02-01
We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.
Physical renormalization schemes and asymptotic safety in quantum gravity
Falls, Kevin
2017-12-01
The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.
International Nuclear Information System (INIS)
Burde, G.I.
2002-01-01
A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given
Lie groups, differential equations, and geometry advances and surveys
2017-01-01
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
Hadamard and minimal renormalizations
International Nuclear Information System (INIS)
Castagnino, M.A.; Gunzig, E.; Nardone, P.; Paz, J.P.
1986-01-01
A common language is introduced to study two, well-known, different methods for the renormalization of the energy-momentum tensor of a scalar neutral quantum field in curved space-time. Different features of the two renormalizations are established and compared
Parallel solutions of the two-group neutron diffusion equations
International Nuclear Information System (INIS)
Zee, K.S.; Turinsky, P.J.
1987-01-01
Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations
International Nuclear Information System (INIS)
Keitel, Jan; Bartosch, Lorenz
2012-01-01
We consider the zero-dimensional O(N) vector model as a simple example to calculate n-point correlation functions using perturbation theory, the large-N expansion and the functional renormalization group (FRG). Comparing our findings with exact results, we show that perturbation theory breaks down for moderate interactions for all N, as one should expect. While the interaction-induced shift of the free energy and the self-energy are well described by the large-N expansion even for small N, this is not the case for higher order correlation functions. However, using the FRG in its one-particle irreducible formalism, we see that very few running couplings suffice to get accurate results for arbitrary N in the strong coupling regime, outperforming the large-N expansion for small N. We further remark on how the derivative expansion, a well-known approximation strategy for the FRG, reduces to an exact method for the zero-dimensional O(N) vector model. (paper)
Prodhan, Suryoday; Ramasesha, S.
2018-05-01
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
Vlad, Marcel Ovidiu; Tsuchiya, Masa; Oefner, Peter; Ross, John
2002-01-01
We investigate the statistical properties of systems with random chemical composition and try to obtain a theoretical derivation of the self-similar Dirichlet distribution, which is used empirically in molecular biology, environmental chemistry, and geochemistry. We consider a system made up of many chemical species and assume that the statistical distribution of the abundance of each chemical species in the system is the result of a succession of a variable number of random dilution events, which can be described by using the renormalization-group theory. A Bayesian approach is used for evaluating the probability density of the chemical composition of the system in terms of the probability densities of the abundances of the different chemical species. We show that for large cascades of dilution events, the probability density of the composition vector of the system is given by a self-similar probability density of the Dirichlet type. We also give an alternative formal derivation for the Dirichlet law based on the maximum entropy approach, by assuming that the average values of the chemical potentials of different species, expressed in terms of molar fractions, are constant. Although the maximum entropy approach leads formally to the Dirichlet distribution, it does not clarify the physical origin of the Dirichlet statistics and has serious limitations. The random theory of dilution provides a physical picture for the emergence of Dirichlet statistics and makes it possible to investigate its validity range. We discuss the implications of our theory in molecular biology, geochemistry, and environmental science.
Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime
International Nuclear Information System (INIS)
Leen, T.K.
1983-01-01
In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space
Non-perturbative quark mass renormalization
Capitani, S.; Luescher, M.; Sint, S.; Sommer, R.; Weisz, P.; Wittig, H.
1998-01-01
We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $\\Lambda$--parameter in this theory with completely controlled errors.
Lee, Eunjung
2013-01-01
The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Group-theoretical interpretation of the Korteweg-de Vries type equations
International Nuclear Information System (INIS)
Berezin, F.A.; Perelomov, A.M.
1978-01-01
The Korteweg-de Vries equation is studied within the group-theoretical framework. Analogous equations are obtained for which the many-dimensional Schroedinger equation (with nonlocal potential) plays the same role as the one-dimensional Schroedinger equation does in the theory of the Korteweg-de Vries equation
Finite size scaling and phenomenological renormalization
International Nuclear Information System (INIS)
Derrida, B.; Seze, L. de; Vannimenus, J.
1981-05-01
The basic equations of the phenomenological renormalization method are recalled. A simple derivation using finite-size scaling is presented. The convergence of the method is studied analytically for the Ising model. Using this method we give predictions for the 2d bond percolation. Finally we discuss how the method can be applied to random systems
Roemelt, Michael; Krewald, Vera; Pantazis, Dimitrios A
2018-01-09
The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.
Energy Technology Data Exchange (ETDEWEB)
Kitahara, Teppei [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, Karlsruhe, D-76128 (Germany); Institute for Nuclear Physics (IKP), Karlsruhe Institute of Technology,Hermann-von-Helmholtz-Platz 1, Eggenstein-Leopoldshafen, D-76344 (Germany); Nierste, Ulrich; Tremper, Paul [Institute for Theoretical Particle Physics (TTP), Karlsruhe Institute of Technology,Engesserstraße 7, Karlsruhe, D-76128 (Germany)
2016-12-16
The standard analytic solution of the renormalization group (RG) evolution for the ΔS=1 Wilson coefficients involves several singularities, which complicate analytic solutions. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of ϵ{sub K}{sup ′}, the measure of direct CP violation in K→ππ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio ϵ{sub K}{sup ′}/ϵ{sub K} (with ϵ{sub K} quantifying indirect CP violation) in the Standard Model (SM) at NLO to ϵ{sub K}{sup ′}/ϵ{sub K}=(1.06±5.07)×10{sup −4}, which is 2.8 σ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximate formulae. We find that the RG amplification of new-physics contributions to Wilson coefficients of the electroweak penguin operators is further enhanced by the NLO corrections: if the new contribution is generated at the scale of 1–10 TeV, the RG evolution between the new-physics scale and the electroweak scale enhances these coefficients by 50–100%. Our solution contains a term of order α{sub EM}{sup 2}/α{sub s}{sup 2}, which is numerically unimportant for the SM case but should be included in studies of high-scale new-physics.
Functional renormalisation group equations for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Synatschke-Czerwonka, Franziska
2011-01-11
This work is organised as follows: In chapter 2 the basic facts of quantum field theory are collected and the functional renormalisation group equations are derived. Chapter 3 gives a short introduction to the main concepts of supersymmetry that are used in the subsequent chapters. In chapter 4 the functional RG is employed for a study of supersymmetric quantum mechanics, a supersymmetric model which are studied intensively in the literature. A lot of results have previously been obtained with different methods and we compare these to the ones from the FRG. We investigate the N=1 Wess-Zumino model in two dimensions in chapter 5. This model shows spontaneous supersymmetry breaking and an interesting fixed-point structure. Chapter 6 deals with the three dimensional N=1 Wess-Zumino model. Here we discuss the zero temperature case as well as the behaviour at finite temperature. Moreover, this model shows spontaneous supersymmetry breaking, too. In chapter 7 the two-dimensional N=(2,2) Wess-Zumino model is investigated. For the superpotential a non-renormalisation theorem holds and thus guarantees that the model is finite. This allows for a direct comparison with results from lattice simulations. (orig.)
Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
Guagnelli, M; Peña, C; Sint, S; Vladikas, A
2006-01-01
We define a family of Schroedinger Functional renormalization schemes for the four-quark multiplicatively renormalizable operators of the $\\Delta F = 1$ and $\\Delta F = 2$ effective weak Hamiltonians. Using the lattice regularization with quenched Wilson quarks, we compute non-perturbatively the renormalization group running of these operators in the continuum limit in a large range of renormalization scales. Continuum limit extrapolations are well controlled thanks to the implementation of two fermionic actions (Wilson and Clover). The ratio of the renormalization group invariant operator to its renormalized counterpart at a low energy scale, as well as the renormalization constant at this scale, is obtained for all schemes.
Renormalization of fermion mixing
International Nuclear Information System (INIS)
Schiopu, R.
2007-01-01
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Renormalization of fermion mixing
Energy Technology Data Exchange (ETDEWEB)
Schiopu, R.
2007-05-11
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation
International Nuclear Information System (INIS)
Wu Guocheng
2011-01-01
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Dimensional renormalization and comparison of renormalization schemes in quantum electrodynamics
International Nuclear Information System (INIS)
Coquereaux, R.
1979-02-01
The method of dimensional renormalization as applied to quantum electrodynamics is discussed. A general method is given which allows one to compare the various quantities like coupling constants and masses that appear in different renormalization schemes
On renormalization of axial anomaly
International Nuclear Information System (INIS)
Efremov, A.V.; Teryaev, O.V.
1989-01-01
It is shown that multiplicative renormalization of the axial singlet current results in renormalization of the axial anomaly in all orders of perturbation theory. It is a necessary condition for the Adler - Bardeen theorem being valid. 10 refs.; 2 figs
Hypercuboidal renormalization in spin foam quantum gravity
Bahr, Benjamin; Steinhaus, Sebastian
2017-06-01
In this article, we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion paper, in which the existence of a fixed point in the truncated renormalization group flow for the model was reported. Here, we repeat the analysis with various modifications and find that both qualitative and quantitative features of the fixed point are robust in this setting. We also go into details about the various approximation schemes employed in the analysis.
Zhou, L.-Q.; Meleshko, S. V.
2017-07-01
The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.
Renormalization of Extended QCD2
International Nuclear Information System (INIS)
Fukaya, Hidenori; Yamamura, Ryo
2015-01-01
Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region
Renormalization of Hamiltonian QCD
International Nuclear Information System (INIS)
Andrasi, A.; Taylor, John C.
2009-01-01
We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang-Mills electric field.
Nonlinear Schroedinger equation with U(p,q) isotopical group
International Nuclear Information System (INIS)
Makhankov, V.G.; Pashaev, O.K.
1981-01-01
The properties of the nonlinear Schroedinger equation (NLS) with U(1,1) isogroup are considered in detail. This example illustrates the essential difference between the system and the well-known ''vector'' NLS, i.e. the large set of allowed boundary conditions on the fields that leads to a rich set of solutions of the system. Four types of boundary conditions and related soliton solutions are considered. The Bohr-Sommerfeld quantization allows to interpret them in terms of ''drops'' and ''bubbles'' as bound states of a large number of constituent bosons subject to the thermodynamical relations for gas mixtures. The U(1,1) system under the vanishing boundary conditions may be considered as continuous analog of the Hubbard model and therefore the paper is concluded by studying the inverse scattering equations for this case [ru
Renormalization of gauge theories without cohomology
International Nuclear Information System (INIS)
Anselmi, Damiano
2013-01-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)
A note on nonperturbative renormalization of effective field theory
Energy Technology Data Exchange (ETDEWEB)
Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China)
2009-08-28
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.
A note on nonperturbative renormalization of effective field theory
International Nuclear Information System (INIS)
Yang Jifeng
2009-01-01
Within the realm of contact potentials, the key structures intrinsic of nonperturbative renormalization of T-matrices are unraveled using rigorous solutions and an inverse form of the algebraic Lippmann-Schwinger equation. The intrinsic mismatches between effective field theory power counting and nonperturbative divergence structures are shown for the first time to preclude the conventional counterterm algorithm from working in the renormalization of EFT for NN scattering in nonperturbative regimes.
Quantum group and symmetry of the heat equation
International Nuclear Information System (INIS)
Jha, P.K.; Tripathy, K.C.
1992-07-01
The symmetry associated with the heat equation is re-examined using Lie's method. Under suitable choice of the arbitrary parameters in the Lie field, it is shown that the system exhibits SL(2,R) symmetry. On inspection of the q-analogue of the principal solution, we find broadening of the Gaussian-flow curve when q is varied from 1 to 0.002. The q-analogue of the general solution predicts the existence of additional degeneracy. (author). 8 refs, 1 fig
He, Yong
2013-01-01
Common test items play an important role in equating multiple test forms under the common-item nonequivalent groups design. Inconsistent item parameter estimates among common items can lead to large bias in equated scores for IRT true score equating. Current methods extensively focus on detection and elimination of outlying common items, which…
Evaluating Equating Accuracy and Assumptions for Groups that Differ in Performance
Powers, Sonya; Kolen, Michael J.
2014-01-01
Accurate equating results are essential when comparing examinee scores across exam forms. Previous research indicates that equating results may not be accurate when group differences are large. This study compared the equating results of frequency estimation, chained equipercentile, item response theory (IRT) true-score, and IRT observed-score…
Renormalization (and power counting) of effective field theories for the nuclear force
International Nuclear Information System (INIS)
Timoteo, Varese S.; Szpigel, Sergio; Duraes, Francisco O.
2011-01-01
The most common scheme used to regularize the Lippman-Schwinger (LS) equation is to introduce a sharp or smooth regularizing function that suppresses the contributions from the potential matrix elements for momenta larger than a given cutoff scale, which separates high-energy/short-distance scales and low-energy/long-distance scales, thus eliminating the ultraviolet divergences in the momentum integrals. Then, one needs determine the strengths of the contact interactions, the so called low-energy constants (LEC), by fitting a set of low-energy scattering data. Once the LECs are fixed for a given cutoff, the LS equation can be solved to evaluate other observables. Such a procedure, motivated by Wilsons renormalization group, relies on the fundamental premise of EFT that physics at low-energy/long-distance scales is insensitive with respect to the details of the dynamics at high-energy/short-distance scales, i.e. the relevant high-energy/short- distance effects for describing the low-energy observables can be captured in the cutoff-dependent LECs. The NN interaction can be considered properly renormalized when the calculated observables are independent of the cutoff scale within the range of validity of the ChEFT or involves a small residual cutoff dependence due to the truncation of the chiral expansion. In the language of Wilsons renormalization group, this means that the LECs must run with the cutoff scale in such a way that the scattering amplitude becomes renormalization group invariant (RGI). Here we consider pionless EFT up to NNLO and chiral EFT up to NNLO and use a subtractive renormalization scheme to describe the NN scattering channels with. We fix the strength of the contact interactions at a reference scale, chosen to be the one the provides the best fit, and then evolve the driving terms with a non-relativistic Callan-Symanzik equation to slide the renormalization scale. By computing phase shift relative differences, we show that the method is RGI. We
Modified two-fluid model for the two-group interfacial area transport equation
International Nuclear Information System (INIS)
Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.
2003-01-01
This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model
Renormalization and asymptotic freedom in quantum gravity
International Nuclear Information System (INIS)
Tomboulis, E.T.
1984-01-01
The article reviews some recent attempts to construct satisfactory theories of quantum gravity within the framework of local, continuum field theory. Quantum gravity; the renormalization group and its fixed points; fixed points and dimensional continuation in gravity; and quantum gravity at d=4-the 1/N expansion-asymptotic freedom; are all discussed. (U.K.)
Renormalizing Entanglement Distillation
Waeldchen, Stephan; Gertis, Janina; Campbell, Earl T.; Eisert, Jens
2016-01-01
Entanglement distillation refers to the task of transforming a collection of weakly entangled pairs into fewer highly entangled ones. It is a core ingredient in quantum repeater protocols, which are needed to transmit entanglement over arbitrary distances in order to realize quantum key distribution schemes. Usually, it is assumed that the initial entangled pairs are identically and independently distributed and are uncorrelated with each other, an assumption that might not be reasonable at all in any entanglement generation process involving memory channels. Here, we introduce a framework that captures entanglement distillation in the presence of natural correlations arising from memory channels. Conceptually, we bring together ideas from condensed-matter physics—ideas from renormalization and matrix-product states and operators—with those of local entanglement manipulation, Markov chain mixing, and quantum error correction. We identify meaningful parameter regions for which we prove convergence to maximally entangled states, arising as the fixed points of a matrix-product operator renormalization flow.
International Nuclear Information System (INIS)
Zhi Hongyan
2009-01-01
In this paper, based on the symbolic computing system Maple, the direct method for Lie symmetry groups presented by Sen-Yue Lou [J. Phys. A: Math. Gen. 38 (2005) L129] is extended from the continuous differential equations to the differential-difference equations. With the extended method, we study the well-known differential-difference KP equation, KZ equation and (2+1)-dimensional ANNV system, and both the Lie point symmetry groups and the non-Lie symmetry groups are obtained.
Holographic renormalization and supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Genolini, Pietro Benetti [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom); Cassani, Davide [LPTHE, Sorbonne Universités UPMC Paris 6 and CNRS, UMR 7589,F-75005, Paris (France); Martelli, Dario [Department of Mathematics, King’s College London,The Strand, London, WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford,Woodstock Road, Oxford OX2 6GG (United Kingdom)
2017-02-27
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N=2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.
Directory of Open Access Journals (Sweden)
Decio Levi
2013-10-01
Full Text Available We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry preserving discretization provides difference schemes for which the “first differential approximation” is invariant under the same Lie group as the original ordinary differential equation.
What is new in the study of differential equations by group theoretical methods
International Nuclear Information System (INIS)
Winternitz, P.
1986-11-01
Several recent developments have made the application of group theory to the solving of differential equations more powerful than it used to be. The ones discussed here are: 1. The advent of symbol manipulating computer languages that greatly simplify the construction of the symmetry group of an equation 2. Methods of finding all subgroups of a given Lie symmetry group 3. The theory of infinite dimensional Lie algebras 4. The combination of group theory and singularity analysis
Renormalization of Supersymmetric QCD on the Lattice
Costa, Marios; Panagopoulos, Haralambos
2018-03-01
We perform a pilot study of the perturbative renormalization of a Supersymmetric gauge theory with matter fields on the lattice. As a specific example, we consider Supersymmetric N=1 QCD (SQCD). We study the self-energies of all particles which appear in this theory, as well as the renormalization of the coupling constant. To this end we compute, perturbatively to one-loop, the relevant two-point and three-point Green's functions using both dimensional and lattice regularizations. Our lattice formulation involves theWilson discretization for the gluino and quark fields; for gluons we employ the Wilson gauge action; for scalar fields (squarks) we use naive discretization. The gauge group that we consider is SU(Nc), while the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, are left unspecified. We obtain analytic expressions for the renormalization factors of the coupling constant (Zg) and of the quark (ZΨ), gluon (Zu), gluino (Zλ), squark (ZA±), and ghost (Zc) fields on the lattice. We also compute the critical values of the gluino, quark and squark masses. Finally, we address the mixing which occurs among squark degrees of freedom beyond tree level: we calculate the corresponding mixing matrix which is necessary in order to disentangle the components of the squark field via an additional finite renormalization.
Renormalization in self-consistent approximation schemes at finite temperature I: theory
International Nuclear Information System (INIS)
Hees, H. van; Knoll, J.
2001-07-01
Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local counter-terms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym's Φ-derivable concept. The scheme generates both, the renormalized self-consistent equations of motion and the closed equations for the infinite set of counter terms. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized, in consistency with the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renormalized approximation scheme to hold. The proof uses the techniques of BPHZ-renormalization to cope with the explicit and the hidden overlapping vacuum divergences. (orig.)
Some Diophantine equations from finite group theory: $\\Phi_m (x) = 2p^n -1$
Luca, F.; Moree, P.; Weger, de B.M.M.
2009-01-01
We show that the equation in the title (with Fn the nth cyclotomic polynomial) has no integer solution with n = 1 in the cases (m, p) = (15, 41), (15, 5581), (10, 271). These equations arise in a recent group theoretical investigation by Z. Akhlaghi, M. Khatami and B. Khosravi.
Some Diophantine equations from finite group theory: $\\Phi_m (x) = 2p^n -1$
Luca, F.; Moree, P.; Weger, de B.M.M.
2011-01-01
We show that the equation in the title (with $\\Psi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n \\geq 1$ in the cases (m,p) = (15,41), (15,5581), (10,271). These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami.
Homotopy analysis solutions of point kinetics equations with one delayed precursor group
International Nuclear Information System (INIS)
Zhu Qian; Luo Lei; Chen Zhiyun; Li Haofeng
2010-01-01
Homotopy analysis method is proposed to obtain series solutions of nonlinear differential equations. Homotopy analysis method was applied for the point kinetics equations with one delayed precursor group. Analytic solutions were obtained using homotopy analysis method, and the algorithm was analysed. The results show that the algorithm computation time and precision agree with the engineering requirements. (authors)
Renormalization method and singularities in the theory of Langmuir turbulence
International Nuclear Information System (INIS)
Pelletier, G.
1977-01-01
The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. This improved renormalization is emphasized. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion. (author)
Phases of renormalized lattice gauge theories with fermions
International Nuclear Information System (INIS)
Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)
1979-01-01
Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory
Do group-specific equations provide the best estimates of stature?
Albanese, John; Osley, Stephanie E; Tuck, Andrew
2016-04-01
An estimate of stature can be used by a forensic anthropologist with the preliminary identification of an unknown individual when human skeletal remains are recovered. Fordisc is a computer application that can be used to estimate stature; like many other methods it requires the user to assign an unknown individual to a specific group defined by sex, race/ancestry, and century of birth before an equation is applied. The assumption is that a group-specific equation controls for group differences and should provide the best results most often. In this paper we assess the utility and benefits of using group-specific equations to estimate stature using Fordisc. Using the maximum length of the humerus and the maximum length of the femur from individuals with documented stature, we address the question: Do sex-, race/ancestry- and century-specific stature equations provide the best results when estimating stature? The data for our sample of 19th Century White males (n=28) were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century any, and 20th Century Hispanic males. The equations were assessed for utility in any one case (how many times the estimated range bracketed the documented stature) and in aggregate using 1-way ANOVA and other approaches. This group-specific equation that should have provided the best results was outperformed by several other equations for both the femur and humerus. These results suggest that group-specific equations do not provide better results for estimating stature while at the same time are more difficult to apply because an unknown must be allocated to a given group before stature can be estimated. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.
Solution of two group neutron diffusion equation by using homotopy analysis method
International Nuclear Information System (INIS)
Cavdar, S.
2010-01-01
The Homotopy Analysis Method (HAM), proposed in 1992 by Shi Jun Liao and has been developed since then, is based on differential geometry as well as homotopy which is a fundamental concept in topology. It has proved to be useful for obtaining series solutions of many such problems involving algebraic, linear/non-linear, ordinary/partial differential equations, differential-integral equations, differential-difference equations, and coupled equations of them. Briefly, through HAM, it is possible to construct a continuous mapping of an initial guess approximation to the exact solution of the equation of concern. An auxiliary linear operator is chosen to construct such kind of a continuous mapping and an auxiliary parameter is used to ensure the convergence of series solution. We present the solutions of two-group neutron diffusion equation through HAM in this work. We also compare the results with that obtained by other well-known solution analytical and numeric methods.
Applications of Lie-group methods to the equations of magnetohydrodynamics
International Nuclear Information System (INIS)
Mandrekas, J.
1987-01-01
The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: the problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time
International Nuclear Information System (INIS)
Foroutan, A.
1992-05-01
The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)
Hardouin, Charlotte; Minchenko, Andrei; Ovchinnikov, Alexey
2015-01-01
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the representation theory of linear differential algebraic groups and develop new algorithms that calculate unipotent radicals of parameterized differential Galois groups for differential equations whose coefficients are rational functions. P. Berman and M.F. Singer ...
Multiplicative renormalizability and self-consistent treatments of the Schwinger-Dyson equations
International Nuclear Information System (INIS)
Brown, N.; Dorey, N.
1989-11-01
Many approximations to the Schwinger-Dyson equations place constraints on the renormalization constants of a theory. The requirement that the solutions to the equations be multiplicatively renormalizable also places constraints on these constants. Demanding that these two sets of constraints be compatible is an important test of the self-consistency of the approximations made. We illustrate this idea by considering the equation for the fermion propagator in massless quenched quantum electrodynamics, (QED), checking the consistency of various approximations. In particular, we show that the much used 'ladder' approximation is self-consistent, provided that the coupling constant is renormalized in a particular way. We also propose another approximation which satisfies this self-consistency test, but requires that the coupling be unrenormalized, as should be the case in the full quenched approximation. This new approximation admits an exact solution, which also satisfies the renormalization group equation for the quenched approximation. (author)
Loop optimization for tensor network renormalization
Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.
Renormalization of gauge theories
International Nuclear Information System (INIS)
Becchi, C.; Rouet, A.; Stora, R.
1975-04-01
Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semi-simple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independant from the parameters which define the gauge function [fr
Renormalized Lie perturbation theory
International Nuclear Information System (INIS)
Rosengaus, E.; Dewar, R.L.
1981-07-01
A Lie operator method for constructing action-angle transformations continuously connected to the identity is developed for area preserving mappings. By a simple change of variable from action to angular frequency a perturbation expansion is obtained in which the small denominators have been renormalized. The method is shown to lead to the same series as the Lagrangian perturbation method of Greene and Percival, which converges on KAM surfaces. The method is not superconvergent, but yields simple recursion relations which allow automatic algebraic manipulation techniques to be used to develop the series to high order. It is argued that the operator method can be justified by analytically continuing from the complex angular frequency plane onto the real line. The resulting picture is one where preserved primary KAM surfaces are continuously connected to one another
Renormalized plasma turbulence theory: A quasiparticle picture
International Nuclear Information System (INIS)
DuBois, D.F.
1981-01-01
A general renormalized statistical theory of Vlasov turbulence is given which proceeds directly from the Vlasov equation and does not assume prior knowledge of sophisticated field-theoretic techniques. Quasiparticles are the linear excitations of the turbulent system away from its instantaneous mean (ensemble-averaged) state or background; the properties of this background state ''dress'' or renormalize the quasiparticle responses. It is shown that all two-point responses (including the dielectric) and all two-point correlation functions can be completely described by the mean distribution function and three fundamental quantities. Two of these are the quasiparticle responses: the propagator and the potential source: which measure, respectively, the separate responses of the mean distribution function and the mean electrostatic potential to functional changes in an external phase-space source added to Vlasov's equation. The third quantity is the two-point correlation function of the incoherent part of the phase-space density which acts as a self-consistent source of quasiparticle and potential fluctuations. This theory explicitly takes into account the self-consistent nature of the electrostatic-field fluctuations which introduces new effects not found in the usual ''test-particle'' theories. Explicit equations for the fundamental quantities are derived in the direct interaction approximation. Special attention is paid to the two-point correlations and the relation to theories of phase-space granulation
General renormalized statistical approach with finite cross-field correlations
International Nuclear Information System (INIS)
Vakulenko, M.O.
1992-01-01
The renormalized statistical approach is proposed, accounting for finite correlations of potential and magnetic fluctuations. It may be used for analysis of a wide class of nonlinear model equations describing the cross-correlated plasma states. The influence of a cross spectrum on stationary potential and magnetic ones is investigated. 10 refs. (author)
International Nuclear Information System (INIS)
Grigoriev, Yurii N; Meleshko, Sergey V; Suriyawichitseranee, Amornrat
2015-01-01
Group analysis of the spatially homogeneous and molecular energy dependent Boltzmann equations with source term is carried out. The Fourier transform of the Boltzmann equation with respect to the molecular velocity variable is considered. The correspondent determining equation of the admitted Lie group is reduced to a partial differential equation for the admitted source. The latter equation is analyzed by an algebraic method. A complete group classification of the Fourier transform of the Boltzmann equation with respect to a source function is given. The representation of invariant solutions and corresponding reduced equations for all obtained source functions are also presented. (paper)
Semi-groups of operators and some of their applications to partial differential equations
International Nuclear Information System (INIS)
Kisynski, J.
1976-01-01
Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)
Analysis of coined quantum walks with renormalization
Boettcher, Stefan; Li, Shanshan
2018-01-01
We introduce a framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights into the analytic structure as well as generic results about the long-time behavior can be extracted. The RG flow for such a walk on a dual Sierpinski gasket and a Migdal-Kadanoff hierarchical network is obtained explicitly from elementary algebraic manipulations, after transforming the unitary evolution equation into Laplace space. Unlike for classical random walks, we find that the long-time asymptotics for the quantum walk requires consideration of a diverging number of Laplace poles, which we demonstrate exactly for the closed-form solution available for the walk on a one-dimensional loop. In particular, we calculate the probability of the walk to overlap with its starting position, which oscillates with a period that scales as NdwQ/df with system size N . While the largest Jacobian eigenvalue λ1 of the RG flow merely reproduces the fractal dimension, df=log2λ1 , the asymptotic analysis shows that the second Jacobian eigenvalue λ2 becomes essential to determine the dimension of the quantum walk via dwQ=log2√{λ1λ2 } . We trace this fact to delicate cancellations caused by unitarity. We obtain identical relations for other networks, although the details of the RG analysis may exhibit surprisingly distinct features. Thus, our conclusions—which trivially reproduce those for regular lattices with translational invariance with df=d and dwQ=1 —appear to be quite general and likely apply to networks beyond those studied here.
Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance
Motsepa, Tanki; Khalique, Chaudry Masood; Molati, Motlatsi
2014-01-01
We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant so...
Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance
Directory of Open Access Journals (Sweden)
Tanki Motsepa
2014-01-01
Full Text Available We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.
Solution of two energy-group neutron diffusion equation by triangular elements
International Nuclear Information System (INIS)
Correia Filho, A.
1981-01-01
The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt
International Nuclear Information System (INIS)
Sheftel', M.B.
1997-01-01
The basics of modern group analysis of different equations are presented. The group analysis produces in a natural way the variables, which are most suitable for a problem of question, and also the associated differential-geometric structures, such as pseudo Riemann geometry, connections, Hamiltonian and Lagrangian formalism
Numerical solution of multi groups point kinetic equations by simulink toolbox of Matlab software
International Nuclear Information System (INIS)
Hadad, K.; Mohamadi, A.; Sabet, H.; Ayobian, N.; Khani, M.
2004-01-01
The simulink toolbox of Matlab Software was employed to solve the point kinetics equation with six group delayed neutrons. The method of Adams-Bash ford showed a good convergence in solving the system of simultaneous equations and the obtained results showed good agreements with other numerical schemes. The flexibility of the package in changing the system parameters and the user friendly interface makes this approach a reliable educational package in revealing the affects of reactivity changes on power incursions
A general analytical approach to the one-group, one-dimensional transport equation
International Nuclear Information System (INIS)
Barichello, L.B.; Vilhena, M.T.
1993-01-01
The main feature of the presented approach to solve the neutron transport equation consists in the application of the Laplace transform to the discrete ordinates equations, which yields a linear system of order N to be solved (LTS N method). In this paper this system is solved analytically and the inversion is performed using the Heaviside expansion technique. The general formulation achieved by this procedure is then applied to homogeneous and heterogeneous one-group slab-geometry problems. (orig.) [de
Differential renormalization of gauge theories
International Nuclear Information System (INIS)
Aguila, F. del; Perez-Victoria, M.
1998-01-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author)
Differential renormalization of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab
Practical algebraic renormalization
International Nuclear Information System (INIS)
Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias
2001-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ
Renormalization of Hamiltonians
International Nuclear Information System (INIS)
Glazek, S.D.; Wilson, K.G.
1993-01-01
This paper presents a new renormalization procedure for Hamiltonians such as those of light-front field theory. The bare Hamiltonian with an arbitrarily large, but finite cutoff, is transformed by a specially chosen similarity transformation. The similarity transformation has two desirable features. First, the transformed Hamiltonian is band diagonal: in particular, all matrix elements vanish which would otherwise have caused transitions with big energy jumps, such as from a state of bounded energy to a state with an energy of the order of the cutoff. At the same time, neither the similarity transformation nor the transformed Hamiltonian, computed in perturbation theory, contain vanishing or near-vanishing energy denominators. Instead, energy differences in denominators can be replaced by energy sums for purposes of order of magnitude estimates needed to determine cutoff dependences. These two properties make it possible to determine relatively easily the list of counterterms needed to obtain finite low energy results (such as for eigenvalues). A simple model Hamiltonian is discussed to illustrate the method
A predictive group-contribution simplified PC-SAFT equation of state: Application to polymer systems
DEFF Research Database (Denmark)
Tihic, Amra; Kontogeorgis, Georgios; von Solms, Nicolas
2008-01-01
A group-contribution (GC) method is coupled with the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) to predict its characteristic pure compound parameters. The estimation of group contributions for the parameters is based on a parameter...... are the molecular structure of the polymer of interest in terms of functional groups and a single binary interaction parameter for accurate mixture calculations....
An accurate solution of point reactor neutron kinetics equations of multi-group of delayed neutrons
International Nuclear Information System (INIS)
Yamoah, S.; Akaho, E.H.K.; Nyarko, B.J.B.
2013-01-01
Highlights: ► Analytical solution is proposed to solve the point reactor kinetics equations (PRKE). ► The method is based on formulating a coefficient matrix of the PRKE. ► The method was applied to solve the PRKE for six groups of delayed neutrons. ► Results shows good agreement with other traditional methods in literature. ► The method is accurate and efficient for solving the point reactor kinetics equations. - Abstract: The understanding of the time-dependent behaviour of the neutron population in a nuclear reactor in response to either a planned or unplanned change in the reactor conditions is of great importance to the safe and reliable operation of the reactor. In this study, an accurate analytical solution of point reactor kinetics equations with multi-group of delayed neutrons for specified reactivity changes is proposed to calculate the change in neutron density. The method is based on formulating a coefficient matrix of the homogenous differential equations of the point reactor kinetics equations and calculating the eigenvalues and the corresponding eigenvectors of the coefficient matrix. A small time interval is chosen within which reactivity relatively stays constant. The analytical method was applied to solve the point reactor kinetics equations with six-groups delayed neutrons for a representative thermal reactor. The problems of step, ramp and temperature feedback reactivities are computed and the results compared with other traditional methods. The comparison shows that the method presented in this study is accurate and efficient for solving the point reactor kinetics equations of multi-group of delayed neutrons
BPHZ renormalization in configuration space for the A4-model
Pottel, Steffen
2018-02-01
Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann identity is shown for a normal product, which is quadratic in the field operator. The realization of the equation of motion is computed for the interacting field and the relation to parametric differential equations is indicated.
Energy Technology Data Exchange (ETDEWEB)
Goettel, Stefan
2015-05-22
In this thesis, we study two recently developed methods to tackle low-dimensional correlated quantum systems. In the first part, we benchmark the extension of the functional renormalization group to spin-systems. We apply it to the two-dimensional XXZ model and reproduce the prediction for the phase transition from planar to axial ordering at the isotropic point. The interpretation of the critical scale (where the flow of the susceptibility diverges) as the critical temperature of the system can be questioned, since it yields only good results in the Ising limit. Especially near the isotropic point, this interpretation becomes unsatisfactory as the Mermin-Wagner theorem is violated. We discuss several problems of the method and conclude that it should only be used to explore phase diagrams. In the second part, we extend previous works to two-level quantum dots in the Coulomb blockade regime with special hopping matrices in nonequilibrium, e.g., the Kondo model, to the generic form, including ferromagnetic leads, spin-orbit interactions etc. The dot and the transport observables are determined completely by the hybridization matrix, leading to one of our major results that all these models can be mapped to the Anderson impurity model with ferromagnetic leads. We investigate this model with a well-controlled real-time renormalization group approach and justify the results of a poor man's scaling analysis. By using a singular value decomposition of the tunneling matrix we can rotate the model to the anisotropic Kondo model in the high-energy regime to solve the flow equations analytically. With this, we calculate the stationary dot magnetization and the current. The minimum of the magnetization is found to be an ellipsoid as function of the magnetic field, where the stretching factor determines the distance to the scaling limit. Afterwards, we consider the special case of two external reservoirs and the system being in the scaling limit and discuss the golden
Group-theoretical aspects of the discrete sine-Gordon equation
International Nuclear Information System (INIS)
Orfanidis, S.J.
1980-01-01
The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed
An analytical solution for the two-group kinetic neutron diffusion equation in cylindrical geometry
International Nuclear Information System (INIS)
Fernandes, Julio Cesar L.; Vilhena, Marco Tullio; Bodmann, Bardo Ernst
2011-01-01
Recently the two-group Kinetic Neutron Diffusion Equation with six groups of delay neutron precursor in a rectangle was solved by the Laplace Transform Technique. In this work, we report on an analytical solution for this sort of problem but in cylindrical geometry, assuming a homogeneous and infinite height cylinder. The solution is obtained applying the Hankel Transform to the Kinetic Diffusion equation and solving the transformed problem by the same procedure used in the rectangle. We also present numerical simulations and comparisons against results available in literature. (author)
Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method
International Nuclear Information System (INIS)
Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr
2008-01-01
Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code
Nonperturbative Renormalization of Composite Operators with Overlap Fermions
Energy Technology Data Exchange (ETDEWEB)
J.B. Zhang; N. Mathur; S.J. Dong; T. Draper; I. Horvath; F. X. Lee; D.B. Leinweber; K.F. Liu; A.G. Williams
2005-12-01
We compute non-perturbatively the renormalization constants of composite operators on a quenched 16{sup 3} x 28 lattice with lattice spacing a = 0.20 fm for the overlap fermion by using the regularization independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations Z{sub A} = Z{sub V} and Z{sub S} = Z{sub P} and find that they agree well (less than 1%) above {mu} = 1.6 GeV. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the {ovr MS} scheme. The wave-function renormalization Z{sub {psi}} is determined from the vertex function of the axial current and Z{sub A} from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the (pa){sup 2} errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.
A shape dynamical approach to holographic renormalization
Energy Technology Data Exchange (ETDEWEB)
Gomes, Henrique [University of California at Davis, Davis, CA (United States); Gryb, Sean [Utrecht University, Institute for Theoretical Physics, Utrecht (Netherlands); Radboud University Nijmegen, Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen (Netherlands); Koslowski, Tim [University of New Brunswick, Fredericton, NB (Canada); Mercati, Flavio; Smolin, Lee [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)
2015-01-01
We provide a bottom-up argument to derive some known results from holographic renormalization using the classical bulk-bulk equivalence of General Relativity and Shape Dynamics, a theory with spatial conformal (Weyl) invariance. The purpose of this paper is twofold: (1) to advertise the simple classical mechanism, trading off gauge symmetries, that underlies the bulk-bulk equivalence of General Relativity and Shape Dynamics to readers interested in dualities of the type of AdS/conformal field theory (CFT); and (2) to highlight that this mechanism can be used to explain certain results of holographic renormalization, providing an alternative to the AdS/CFT conjecture for these cases. To make contact with the usual semiclassical AdS/CFT correspondence, we provide, in addition, a heuristic argument that makes it plausible that the classical equivalence between General Relativity and Shape Dynamics turns into a duality between radial evolution in gravity and the renormalization group flow of a CFT. We believe that Shape Dynamics provides a new perspective on gravity by giving conformal structure a primary role within the theory. It is hoped that this work provides the first steps toward understanding what this new perspective may be able to teach us about holographic dualities. (orig.)
Renormalization and Interaction in Quantum Field Theory
International Nuclear Information System (INIS)
RATSIMBARISON, H.M.
2008-01-01
This thesis works on renormalization in quantum field theory (QFT), in order to show the relevance of some mathematical structures as C*-algebraic and probabilistic structures. Our work begins with a study of the path integral formalism and the Kreimer-Connes approach in perturbative renormalization, which allows to situate the statistical nature of QFT and to appreciate the ultra-violet divergence problem of its partition function. This study is followed by an emphasis of the presence of convolution products in non perturbative renormalisation, through the construction of the Wilson effective action and the Legendre effective action. Thanks to these constructions and the definition of effective theories according J. Polchinski, the non perturbative renormalization shows in particular the general approach of regularization procedure. We begin the following chapter with a C*-algebraic approach of the scale dependence of physical theories by showing the existence of a hierarchy of commutative spaces of states and its compatibility with the fiber bundle formulation of classical field theory. Our Hierarchy also allows us to modelize the notion of states and particles. Finally, we develop a probabilistic construction of interacting theories starting from simple model, a Bernoulli random processes. We end with some arguments on the applicability of our construction -such as the independence between the free and interacting terms and the possibility to introduce a symmetry group wich will select the type of interactions in quantum field theory. [fr
Renormalized trajectory for non-linear sigma model and improved scaling behaviour
International Nuclear Information System (INIS)
Guha, A.; Okawa, M.; Zuber, J.B.
1984-01-01
We apply the block-spin renormalization group method to the O(N) Heisenberg spin model. Extending a previous work of Hirsch and Shenker, we find the renormalized trajectory for O(infinite) in two dimensions. Four finite N models, we choose a four-parameter action near the large-N renormalized trajectory and demonstrate a remarkable improvement in the approach to continuum limit by performing Monte Carlo simulation of O(3) and O(4) models. (orig.)
On the exact solution for the multi-group kinetic neutron diffusion equation in a rectangle
International Nuclear Information System (INIS)
Petersen, C.Z.; Vilhena, M.T.M.B. de; Bodmann, B.E.J.
2011-01-01
In this work we consider the two-group bi-dimensional kinetic neutron diffusion equation. The solution procedure formalism is general with respect to the number of energy groups, neutron precursor families and regions with different chemical compositions. The fast and thermal flux and the delayed neutron precursor yields are expanded in a truncated double series in terms of eigenfunctions that, upon insertion into the kinetic equation and upon taking moments, results in a first order linear differential matrix equation with source terms. We split the matrix appearing in the transformed problem into a sum of a diagonal matrix plus the matrix containing the remaining terms and recast the transformed problem into a form that can be solved in the spirit of Adomian's recursive decomposition formalism. Convergence of the solution is guaranteed by the Cardinal Interpolation Theorem. We give numerical simulations and comparisons with available results in the literature. (author)
Analysis and applications of a group contribution sPC-SAFT equation of state
DEFF Research Database (Denmark)
Tihic, Amra; von Solms, Nicolas; Michelsen, Michael Locht
2009-01-01
A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L Michelsen, L Constantinou. Ind. En...
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
Tielemans, E.; Kupper, L.L.; Kromhout, H.; Heederik, D.; Houba, R.
1998-01-01
Basically, two strategies can be considered for the analysis of hazardous pollutants in the work environment: group-based and individual-based strategies. This paper provides existing and recently derived equations for both strategies describing the influence of several factors on attenuation and on
Series expansion solution of the Wegner-Houghton renormalisation group equation
International Nuclear Information System (INIS)
Margaritis, A.; Odor, G.; Patkos, A.
1987-11-01
The momentum independent projection of the Wegner-Houghton renormalisation group equation is solved with power series expansion. Convergence rate is analyzed for the n-vector model. Further evidence is presented for the first order nature of the chiral symmetry restoration at finite temperature in QCD with 3 light flavors. (author) 16 refs
International Nuclear Information System (INIS)
Osborn, H.
1991-01-01
A local renormalisation group equation which realises infinitesimal Weyl rescalings of the metric and which is an extension of the usual Callan-Symanzik equation is described. In order to ensure that any local composite operators, with dimensions so that on addition to the basic lagrangian they preserve renormalisability, are well defined for arbitrarily many insertions into correlation functions the couplings are assumed to depend on χ. Local operators are then defined by functional differentiation with respect to the couplings just as the energy-momentum tensor is given by functional differentiation with respect to the metric. The local renormalisation group equation contains terms depending on derivatives of the couplings as well as the curvature tensor formed from the metric, constrained by power counting. Various consistency relations arising from the commutativity of Weyl transformations are derived, extending previous one-loop results for the trace anomaly to all orders. In two dimensions the relations give an alternative derivation of the c-theorem and similar extensions are obtained in four dimensions. The equations are applied in detail to general renormalisable σ-models in two dimensions. The Curci-Paffuti relation is derived without any commitment to a particular regularisation scheme and further equations used to construct an action for the vanishing of the β-functions are also obtained. The discussion is also extended to σ-models with a boundary, as appropriate for open strings, and relations for the additional β-functions present in such models are obtained. (orig.)
International Nuclear Information System (INIS)
Ma Hongcai
2005-01-01
Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.