Anomalous distribution of magnetization in an Ising spin glass with correlated disorder

TL;DR

This paper investigates how correlations in disorder affect the magnetization distribution in spin glasses, revealing unconventional behaviors that challenge existing theories about replica symmetry breaking and phase confinement.

Contribution

It demonstrates that correlated disorder can produce magnetization distributions with support on a finite interval, contrasting with traditional models, and explores implications for phase behavior and disorder effects.

Findings

Magnetization distribution matches the spin glass order parameter distribution.

Correlated disorder leads to magnetization support on a finite interval.

Ferromagnetic phase is confined to the Nishimori line when temperature chaos occurs.

Abstract

The effect of correlations in disorder variables is a largely unexplored topic in spin glass theory. We study this problem through a specific example of correlated disorder introduced in the Ising spin glass model. We prove that the distribution function of the magnetization along the Nishimori line in the present model is identical to the distribution function of the spin glass order parameter in the standard Edwards-Anderson model with symmetrically-distributed independent disorder. This result means that if the Edwards-Anderson model exhibits replica symmetry breaking, the magnetization distribution in the correlated model has support on a finite interval, in sharp contrast to the conventional understanding that the magnetization distribution has at most two delta peaks. This unusual behavior challenges the traditional argument against replica symmetry breaking on the Nishimori line in the Edwards-Anderson model. In addition, we show that when temperature chaos is present in the Edwards-Anderson model, the ferromagnetic phase is strictly confined to the Nishimori line in the present model. These findings are valid not only for finite-dimensional systems but also for the infinite-range model, and highlight the need for a deeper understanding of disorder correlations in spin glass systems.