Hysteresis behavior of the random-field Ising model with 2-spin-flip dynamics: Exact results on a Bethe lattice

TL;DR

This paper provides an exact analysis of hysteresis in the zero-temperature random-field Ising model on a Bethe lattice with 2-spin-flip dynamics, revealing a phase transition at connectivity z=3.

Contribution

It introduces an exact solution for the hysteresis behavior under 2-spin-flip dynamics, highlighting differences from standard 1-spin-flip dynamics and identifying a phase transition.

Findings

Existence of an out-of-equilibrium phase transition at z=3

Differences between 2-spin-flip and 1-spin-flip dynamics

Exact results for hysteresis on Bethe lattices

Abstract

We present an exact treatment of the hysteresis behavior of the zero-temperature random-field Ising model on a Bethe lattice when it is driven by an external field and evolved according to a 2-spin-flip dynamics. We focus on lattice connectivities z=2 (the one-dimensional chain) and z=3. For the latter case, we demonstrate the existence of an out-of-equilibrium phase transition, in contrast with the situation found with the standard 1-spin-flip dynamics. We discuss the influence of the degree of cooperativity of the (local) spin dynamics of the nonequilibrium response on the system.