Dimer mean-field model for the Ising spin glass

TL;DR

This paper introduces a simple dimer mean-field model for the Ising spin glass that captures key features like two temperature scales for the glass transition, the Almeida-Thouless line, and diverging relaxation times.

Contribution

It presents a novel, simplified mean-field approach to spin glasses that reproduces essential glassy phenomena and provides insights into the glass transition and dynamics.

Findings

Identification of two distinct temperature scales for glass transition

Divergence of information compressibility at freezing temperature

Existence of the Almeida-Thouless line in the model

Abstract

A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a self-consistent integral equation. By solving the self-consistency condition numerically, we find that there are two temperature scales characterizing the glass transition. At the first, higher temperature, the glass order parameter becomes non-vanishing, and at the second, freezing temperature, it saturates to its maximal value. The effect of magnetic field and the existence of the Almeida-Thouless line are discussed. Finally, it is shown that the information compressibility, defined as the derivative of entropy with respect to energy, diverges at the freezing temperature. This indicates a zero internal temperature and true glassy dynamics with diverging relaxation times.