Phases of memristive circuits via an interacting disorder approach

TL;DR

This paper analyzes the complex phase behavior of memristive circuits using a novel Lyapunov function, revealing a rich phase diagram with glass and ferromagnetic transitions, indicating intricate asymptotic state landscapes.

Contribution

It introduces a new Lyapunov function approach to study memristive circuits, extending mean-field theory to include interacting quenched disorder effects.

Findings

Discovery of a complex phase diagram with glass and ferromagnetic phases

Identification of a non-trivial landscape of asymptotic states

Extension of mean-field results to more realistic models

Abstract

We study the phase diagram of memristive circuit models in the replica-symmetric case using a novel Lyapunov function for the dynamics of these devices. Effectively, the model we propose is an Ising model with interacting quenched disorder, which we study at the first order in a control parameter. Notwithstanding these limitations, we find a complex phase diagram and a glass-ferromagnetic transition in the parameter space which generalizes earlier mean-field theory results for a simpler model. Our results suggest a non-trivial landscape of asymptotic states for memristive circuits.