Hysteresis and return point memory in the random field Blume Capel model

TL;DR

This paper investigates the hysteresis behavior and return point memory in the zero-temperature steady state of the random field Blume Capel model, using simulations and analytical solutions on different graph structures.

Contribution

It provides the first detailed analysis of hysteresis loops and return point memory in the RFBC model, with analytical solutions on Bethe lattices matching simulations.

Findings

Double hysteresis loops observed in magnetization curves.

Good agreement between simulations and Bethe lattice solutions.

Hysteresis behavior depends on the external field H.

Abstract

We study the zero temperature steady state of the random field Blume Capel model with spin-flip Glauber dynamics on a random regular graph. The magnetization m as a function of the external field H is observed to have double hysteresis loops with a return point memory. We also solve the model on a Bethe lattice in the approximation that the spin relaxation dynamics is abelian and find good agreement between simulations on random regular graphs and Bethe lattice calculations for negative values of H.