Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field

TL;DR

This paper proves that in certain disordered FKG-Ising models under a uniform field, the variance of spin overlap vanishes, indicating no replica symmetry breaking occurs, extending previous Gaussian disorder results to broader distributions.

Contribution

It generalizes Chatterjee's proof for Gaussian disorder to models with various i.i.d. disorder distributions under a uniform field.

Findings

Variance of spin overlap vanishes in these models

No replica symmetry breaking occurs in the studied models

Results extend to non-Gaussian disorder distributions

Abstract

We prove that the variance of spin overlap vanishes in disordered Ising models satisfying the Fortuin-Kasteleyn-Ginibre (FKG) inequality under a uniform field, such as generally distributed random field Ising model, site- and bond-diluted Ising models with the Bernoulli distribution. Chatterjee's proof for the Gaussian random field Ising model is generalized to other independent identically distributed quenched disorder under a uniform field.