Renormalization Group Functions for Two-Dimensional Phase Transitions: To the Problem of Singular Contributions

Abstract

According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the existence of nonanalytic contributions in the RG functions. The situation is analysed in this work using a new algorithm for summing divergent series that makes it possible to analyse dependence of the results for the critical exponents on the expansion coefficients for RG functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonities or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in RG functions.

PDF, 11 pages

References in corpus (4)

• Critical Exponents of the N-vector model
• Four-point renormalized coupling constant and Callan-Symanzik beta-function in O(N) models
• Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) model
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Cited by in corpus (5)

• The nonperturbative functional renormalization group and its applications
• Non-perturbative renormalization group preserving full-momentum dependence: implementation and quantitative evaluation
• Solutions of renormalization group flow equations with full momentum dependence
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Renormalization group flow equations with full momentum dependence