Hysteresis in Anti-Ferromagnetic Random-Field Ising Model at Zero Temperature

TL;DR

This paper investigates hysteresis behavior in a one-dimensional anti-ferromagnetic random-field Ising model at zero temperature, analyzing the effects of different random-field distributions through exact solutions and simulations.

Contribution

It provides exact solutions for hysteresis loops in a 1D anti-ferromagnetic RFIM for two types of random-field distributions, enhancing understanding of disorder effects.

Findings

Exact hysteresis loops are derived for both uniform and Gaussian distributions.

Numerical simulations confirm the analytical results.

The shape of the hysteresis loop depends on the distribution of the random field.

Abstract

We study hysteresis in anti-ferromagnetic random-field Ising model at zero temperature. The external field is cycled adiabatically between -$\infty$ and $\infty$. Two different distributions of the random-field are considered, (i) a uniform distribution of width $2\Delta$ centered at the origin, and (ii) a Gaussian distribution with average value zero and standard deviation $\sigma$. In each case the hysteresis loop is determined exactly in one dimension and compared with numerical simulations of the model.