Ising spin glass models versus Ising models: an effective mapping at high temperature I. General result

TL;DR

This paper demonstrates that at high temperatures and sufficiently high dimensions, Ising spin glass models can be effectively mapped onto simpler Ising models, enabling easier analysis of phase boundaries and correlations.

Contribution

It introduces a general mapping between high-temperature spin glass models and Ising models, providing exact phase boundary calculations in the infinite-dimensional limit.

Findings

Mapping is exact in the infinite-dimensional limit.

Provides simple rules for phase boundary and crossover surface determination.

Applied to various spin glass models with successful results.

Abstract

We show that, above the critical temperature, if the dimension D of a given Ising spin glass model is sufficiently high, its free energy can be effectively expressed through the free energy of a related Ising model. When, in a large sense, D is infinite, in the paramagnetic phase and on its boundary the mapping is exact. In this limit the method provides a general and simple rule to obtain exactly the upper phase boundaries. We provide even simple effective rules to find crossover surfaces and correlation functions. We apply the mapping to several spin glass models.