Phase transitions in two dimensions and multiloop renormalization group expansions

Abstract

We discuss using the field theory renormalization group (RG) to study the critical behavior of twodimensional (2D) models. We write the RG functions of the 2D λϕ4 Euclidean n-vector theory up to five-loop terms, give numerical estimates obtained from these series by Pade-Borel-Leroy resummation, and compare them with their exact counterparts known for n = 1, 0,−1. From the RG series, we then derive pseudo-e-expansions for the Wilson fixed point location g*, critical exponents, and the universal ratio R6 = g6/g2, where g6 is the effective sextic coupling constant. We show that the obtained expansions are “friendler” than the original RG series: the higher-order coefficients of the pseudo-e-expansions for g*, R6, and γ−1 turn out to be considerably smaller than their RG analogues. This allows resumming the pseudo-e-expansions using simple Pade approximants without the Borel-Leroy transformation. Moreover, we find that the numerical estimates obtained using the pseudo-e-expansions for g* and γ−1 are closer to the known exact values than those obtained from the five-loop RG series using the Pade-Borel-Leroy resummation.