A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model

TL;DR

This paper introduces a self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model, enabling analysis of correlation functions and thermodynamics, with exactness in infinite dimensions and potential for finite-dimensional stability studies.

Contribution

It develops a novel approximation method using Legendre transforms in replica space, providing a new approach to study spin glasses beyond mean-field theory.

Findings

Predicted freezing temperature as a function of dimension

Calculated thermodynamic properties above freezing

Provided a numerical framework for stability analysis

Abstract

We propose a self-consistent Ornstein-Zernike approximation for studying the Edwards-Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the numerical predictions for the freezing temperature and the zero-field thermodynamic properties above freezing as a function of dimensionality.