Symmetry Non Restoration and Inverse Symmetry Breaking on the lattice

TL;DR

This paper investigates the symmetry behavior of certain scalar models at finite temperature on the lattice, demonstrating that symmetry is always restored at high temperatures, contrary to some continuum predictions.

Contribution

It proves that symmetry non-restoration and inverse symmetry breaking do not occur on the lattice for these models, contrasting with continuum perturbation theory.

Findings

Symmetry is always restored at high temperatures on the lattice.

Symmetry non-restoration does not occur in lattice models.

Contrasts with continuum perturbation theory predictions.

Abstract

We study the finite temperature symmetry behaviour of O(N_1) \times O(N_2) scalar models on the lattice and we prove that at sufficiently high temperatures and in arbitrary dimensions their full symmetry is always restored or, equivalently, that the phenomenon of Symmetry Non Restoration which, according to lowest order perturbation theory, takes place in the continuum version of these models, does not occur on the lattice.