Return to return point memory

TL;DR

This paper introduces a new class of systems exhibiting return point memory (RPM), focusing on one-dimensional random antiferromagnetic Ising models, revealing conditions under which RPM holds or fails, and proposing a more fundamental variable representation.

Contribution

It demonstrates RPM in antiferromagnetic chains from large fields, shows RPM violation from certain stable configurations, and introduces spin flip variables as a fundamental dynamic representation.

Findings

RPM exists in 1D random antiferromagnets from large fields

RPM is violated from some stable configurations at finite fields

Spin flip variables may be more fundamental for describing dynamics

Abstract

We describe a new class of systems exhibiting return point memory (RPM) that are different from those discussed before in the context of ferromagnets. We show numerically that one dimensional random Ising antiferromagnets have RPM, when configurations evolve from a large field. However, RPM is violated when started from some stable configurations at finite field unlike in the ferromagnetic case. This implies that the standard approach to understanding ferromagnetic RPM systems will fail for this case. We also demonstrate RPM with a set of variables that keep track of spin flips at each site. Conventional RPM for the spin configuration is a projection of this result, suggesting that spin flip variables might be a more fundamental representation of the dynamics. We also present a mapping that embeds the antiferromagnetic chain in a two dimensional ferromagnetic model, and prove RPM for spin exchange dynamics in the interior of the chain with this mapping.