Zero-temperature Hysteresis in Random-field Ising Model on a Bethe Lattice

TL;DR

This paper analyzes the zero-temperature hysteresis behavior of the random-field Ising model on a Bethe lattice, revealing how coordination number influences magnetization discontinuities, with results supported by exact equations and Monte Carlo simulations.

Contribution

It provides exact self-consistent equations for magnetization and demonstrates the impact of lattice coordination on hysteresis discontinuities.

Findings

No magnetization jump for 3-coordinated lattice with small disorder

Discontinuity appears at higher coordination numbers

Monte Carlo simulations confirm theoretical predictions

Abstract

We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus infinity to plus infinity by setting up the self-consistent field equations, which we show are exact in this case. We find that for a 3-coordinated Bethe lattice, there is no jump discontinuity in magnetization for arbitrarily small gaussian disorder, but the discontinuity is present for larger coordination numbers. We have checked our results by Monte Carlo simulations employing a technique for simulating classical interacting systems on the Bethe lattice which avoids surface effects altogether.