Reflection symmetry in mean-field replica-symmetric spin glasses

TL;DR

This paper investigates how reflection symmetry breaking influences the nature of phase transitions in mean-field replica-symmetric spin glasses, establishing a symmetry rule linking pure and random systems' transition types.

Contribution

It introduces a symmetry rule that predicts the emergence of glass regimes based on the order of phase transitions in pure systems within the mean-field approximation.

Findings

Second order transitions in pure systems lead to phase transition-induced glass regimes.

First order transitions in pure systems result in continuous growth of glass and ordered regimes.

The study clarifies the role of reflection symmetry in the behavior of spin glass models.

Abstract

The role of reflection symmetry breaking for the character of the appearance of replica symmetric spin glass state is investigated. We establish the following symmetry rule for classical systems with one order parameter in the replica symmetric mean field approximation. If in the pure system the transition to the ordered phase is of the second order, then in the corresponding random system the glass regime appears as a result of a phase transition; if the transition in the pure system is of the first order, then glass and ordered regimes grow continuously in the random system on cooling.