Topological conditions for discrete symmetry breaking and phase transitions

TL;DR

This paper introduces topological conditions that guarantee symmetry breaking and phase transitions, illustrating them with a simple hypercubic model and analyzing existing mean-field models.

Contribution

It proposes new topological criteria for symmetry breaking, supported by a simple solvable model and application to known mean-field models.

Findings

The hypercubic model demonstrates the sufficiency of the topological conditions.

Topological conditions can predict symmetry-breaking phase transitions.

Application to mean-field models confirms the relevance of the criteria.

Abstract

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here.