Return to return point memory

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.

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• The structure of state transition graphs in hysteresis models with return point memory: I. General Theory
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• Transition Graphs of Interacting Hysterons: Structure, Design, Organization and Statistics
• Distribution of interevent avalanche times in disordered and frustrated spin systems
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• The dynamics of a driven harmonic oscillator coupled to pairwise interacting Ising spins in random fields
• Transients and multiperiodic responses: a hierarchy of material bits