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Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field (1910.03776v2)
Published 9 Oct 2019 in math-ph, cond-mat.dis-nn, and math.MP
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.
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