Five-loop epsilon expansion for O(n)xO(m) spin models

TL;DR

This paper computes high-order perturbative expansions for O(n)xO(m) spin models to determine the boundary of second-order phase transitions and critical exponents, providing precise estimates for physically relevant cases.

Contribution

It presents a five-loop epsilon expansion and re-analysis of six-loop series for O(n)xO(m) models, improving the accuracy of the critical boundary n^+(m,d) and critical exponents.

Findings

n^+(2,3)=6.1(6) from epsilon expansion

n^+(2,3)=6.22(12) from fixed dimension series

Provides predictions for critical exponents for n>n^+.

Abstract

We compute the Renormalization Group functions of a Landau-Ginzburg-Wilson Hamiltonian with O(n)x O(m) symmetry up to five-loop in Minimal Subtraction scheme. The line n^+(m,d), which limits the region of second-order phase transition, is reconstructed in the framework of the epsilon=4-d expansion for generic values of $m$ up to O(epsilon^5). For the physically interesting case of noncollinear but planar orderings (m=2) we obtain n^+(2,3)=6.1(6) by exploiting different resummation procedures. We substantiate this results re-analyzing six-loop fixed dimension series with pseudo-epsilon expansion, obtaining n^+(2,3)=6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n>n^+.