Memristive Ising Circuits

TL;DR

This paper demonstrates that memristive circuits can emulate the Ising model, including both ferromagnetic and antiferromagnetic interactions, enabling new ways to simulate complex magnetic systems with stochastic resistors.

Contribution

It introduces a method to realize Ising interactions in memristive circuits, including co-existing ferromagnetic and antiferromagnetic types, and shows how to extract Ising parameters from circuit statistics.

Findings

Circuit state statistics match Ising model distributions.

Ising Hamiltonian can be reconstructed from circuit data.

Different interaction types are realizable in memristive circuits.

Abstract

The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically-driven circuits of stochastic binary resistors with memory. A key feature of our realization is the simultaneous co-existence of ferromagnetic and antiferromagnetic interactions between two neighboring spins -- an extraordinary property not available in nature. We demonstrate that the statistics of circuit states may perfectly match the ones found in the Ising model with ferromagnetic or antiferromagnetic interactions, and, importantly, the corresponding Ising model parameters can be extracted from the probabilities of circuit states. Using this finding, the Ising Hamiltonian is re-constructed in several model cases, and it is shown that different types of interaction can be realized in circuits of stochastic memristors.