Random-field Ising model on complete graphs and trees

TL;DR

This paper provides exact analysis of the critical behavior of the random-field Ising model on complete graphs and trees, revealing non-universality on complete graphs and universality on Cayley trees across different random field distributions.

Contribution

It offers the first exact results for RFIM critical behavior on these graph structures, highlighting differences in universality properties.

Findings

Behavior on complete graphs is non-universal for certain distributions.

Behavior on Cayley trees is universal regardless of distribution.

Exact results for equilibrium and non-equilibrium states.

Abstract

We present exact results for the critical behavior of the RFIM on complete graphs and trees, both at equilibrium and away from equilibrium, i.e., models for hysteresis and Barkhausen noise. We show that for stretched exponential and power law distributions of random fields the behavior on complete graphs is non-universal, while the behavior on Cayley trees is universal even in the limit of large co-ordination.