Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

TL;DR

This paper reviews the theoretical and numerical aspects of replica symmetry breaking in finite-dimensional spin glasses, highlighting challenges, presenting new results, and discussing the nature of pure states and phase transitions.

Contribution

It offers new theoretical ideas and numerical evidence on RSB in realistic short-range spin glasses, addressing longstanding difficulties in constructing pure states.

Findings

Numerical verification of sum rules in spin glasses

Behavior of coupled replicas analyzed numerically

Identification of phase transition points and correlation functions

Abstract

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).