The Effectiveness of the Local Potential Approximation in the Wegner-Houghton Renormalization Group

Aoki, Kenichi; Morikawa, Keiichi; Souma, Wataru; Sumi, Jun–Ichi; Terao, Haruhiko

doi:10.1143/ptp.95.409

Cited by 63 publications

(82 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The exponent ν is in agreement with the known results at the 1-5 % level, with a discrepancy roughly equal to the value of η for various N. Our results compare well with those obtained by similar methods using a variety of forms for the infrared cutoff function [138,110,104,87,83].…”

Section: ) Is Solved Numerically and η Is Approximated By Eq (45) supporting

confidence: 90%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

View full text Add to dashboard Cite

We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.This work is dedicated to the 60th birthday of Franz Wegner. *

show abstract

Section: ) Is Solved Numerically and η Is Approximated By Eq (45) supporting

confidence: 90%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

View full text Add to dashboard Cite

show abstract

“…As expected η is rather poorly determined since it is the quantity most seriously affected by the omission of the higher derivative terms in the average action. The exponent ν is in agreement with the known results at the 1 % level, with a discrepancy between lowest and first order ((f ) vs. (g)) roughly equal to the value of η for various N. Similar results are found for a variety of forms for the infrared cutoff function [83,26,55,63,84]. We observe a convincing apparent convergence of the derivative expansion towards the high precision values obtained from the other methods.…”

Section: Second-order Phase Transitionssupporting

confidence: 89%

“…For a recent study on convergence properties of the derivative expansion see [53]. 8 See also [49,54,55] for the importance of expanding around φ = φ 0 instead of φ = 0 and refs. [56,57,58].…”

Section: Truncationsmentioning

confidence: 99%

Effective Average Action in Statistical Physics and Quantum Field Theory

Wetterich

2001

Non-Perturbative QFT Methods and Their Applications

View full text Add to dashboard Cite

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N )-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.

show abstract

“…The relevance of such a parametrization is confirmed by many works showing that the convergence of the critical quantities, when more and more powers of the field φ are added in the truncation, is improved when compared with the same calculation performed with an expansion of U k (φ) and Z k (φ) around the φ = 0 configuration [186,187].…”

Section: Truncationsmentioning

confidence: 90%

Nonperturbative renormalization-group approach to frustrated magnets

2004

View full text Add to dashboard Cite

This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

show abstract

The Effectiveness of the Local Potential Approximation in the Wegner-Houghton Renormalization Group

Cited by 63 publications

References 10 publications

Non-perturbative renormalization flow in quantum field theory and statistical physics

Non-perturbative renormalization flow in quantum field theory and statistical physics

Effective Average Action in Statistical Physics and Quantum Field Theory

Nonperturbative renormalization-group approach to frustrated magnets

Contact Info

Product

Resources

About