Critical behavior of O(2)xO(N) symmetric models

TL;DR

This paper investigates the critical behavior and universality classes of three-dimensional O(2)xO(N) symmetric models, combining high-order field-theoretical calculations with Monte Carlo simulations to confirm the existence of stable fixed points and universality classes.

Contribution

It provides the first five-loop field-theoretical analysis confirming stable fixed points for N=2,3 and supports the O(2)xO(2) universality class through Monte Carlo simulations.

Findings

Stable fixed points exist for N=2 and N=3.

Monte Carlo simulations support the O(2)xO(2) universality class.

Field-theoretical results are consistent across different schemes.

Abstract

We investigate the controversial issue of the existence of universality classes describing critical phenomena in three-dimensional statistical systems characterized by a matrix order parameter with symmetry O(2)xO(N) and symmetry-breaking pattern O(2)xO(N) -> O(2)xO(N-2). Physical realizations of these systems are, for example, frustrated spin models with noncollinear order. Starting from the field-theoretical Landau-Ginzburg-Wilson Hamiltonian, we consider the massless critical theory and the minimal-subtraction scheme without epsilon expansion. The three-dimensional analysis of the corresponding five-loop expansions shows the existence of a stable fixed point for N=2 and N=3, confirming recent field-theoretical results based on a six-loop expansion in the alternative zero-momentum renormalization scheme defined in the massive disordered phase. In addition, we report numerical Monte Carlo simulations of a class of three-dimensional O(2)xO(2)-symmetric lattice models. The results provide further support to the existence of the O(2)xO(2) universality class predicted by the field-theoretical analyses.