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

TL;DR

This paper analytically studies the hysteresis behavior in a one-dimensional anti-ferromagnetic random field Ising model at zero-temperature, focusing on the case where the disorder width is less than or equal to the interaction strength.

Contribution

It provides an explicit analytical expression for the hysteresis loop in the specific case where the disorder width does not exceed the interaction strength.

Findings

Analytic expression for hysteresis loop derived

Hysteresis behavior characterized for specific disorder range

Insights into zero-temperature anti-ferromagnetic systems obtained

Abstract

We analyse hysteresis in a one-dimensional anti-ferromagnetic random field Ising model at zero-temperature. The random field is taken to have a rectangular distribution of width $2 \Delta$ centered about the origin. A uniform applied field is varied slowly from $-\infty$ to $+\infty$ and back. Analytic expression for the hysteresis loop is obtained in the case $\Delta \le |J|$, where $|J|$ is the strength of the nearest neighbor interaction.