A general method to determine replica symmetry breaking transitions

TL;DR

The paper introduces a new parameter for analyzing replica symmetry breaking transitions in spin glasses, applicable to models with or without time reversal symmetry, enhancing finite-size scaling methods.

Contribution

It presents a novel parameter based on Guerra's equalities for detecting replica symmetry breaking transitions, especially in models lacking time reversal symmetry.

Findings

Effective in models with time reversal symmetry.

Useful for models without time reversal symmetry.

Applicable to various spin glass models, including long-range and short-range.

Abstract

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest concerns models where this symmetry is absent. We apply the method to long-range and short-range Ising spin glasses with and without magnetic field as well as short-range multispin interaction spin glasses.