Exact calculation of the energy contributions to the T=0 random-field Ising model with metastable dynamics on the Bethe lattice

TL;DR

This paper provides exact calculations of energy contributions in the zero-temperature random-field Ising model on the Bethe lattice, revealing how disorder and lattice coordination influence the system's energy landscape and phase transition behavior.

Contribution

It introduces exact analytical expressions for energy terms in the RFIM with metastable dynamics on the Bethe lattice, validated by numerical simulations.

Findings

Exact energy calculations as a function of disorder and coordination number

Identification of disorder-induced phase transition at z=4

Good agreement between analytical results and simulations

Abstract

We analyze the energy terms corresponding to the spin-spin exchange and spin-random field coupling of the zero temperature random-field Ising model on the Bethe lattice driven by an external field with metastable dynamics. Exact results are calculated as a function of the standard deviation of the disorder and the coordination number z, and compared with numerical simulations on random graphs for z=4, for which a disorder-induced transition takes place.