Return-point memory of the random field Ising model at zero temperature in the mean-field approximation

Abstract

The random field Ising model at zero temperature (RFIM T=0) is a paradigmatic model of hysteresis and memory of driven extended disordered systems. Under quasistatic driving these systems display interesting properties such as return-point memory (RPM) of partial cycles. Here we show how to solve the T=0 RFIM in the mean-field approximation, and prove that in this simple approximation the model still displays hysteresis, though only for sufficiently narrow distributions of random fields. We simulate partial hysteresis cycles and first-order reversal curves (FORC) for this case, and show that the T=0 RFIM in the mean-field approximation verifies also the RPM.