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

Abstract

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