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

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.

arXiv comment14 pages

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Cited by in corpus (2)

• Uniqueness of ground state in the Edwards-Anderson spin glass model
• On the Ultrametricity Property in Random Field Ising Models