A Combinatorial Perspective on Ising Model Hysteresis

In this work, we apply combinatorial methods used extensively in Artificial Intelligence (AI) to understand Ising model hysteresis. Our approach is based on efficiently generating the top K solutions of the Ising model and its generalization in AI, called the Weighted Constraint Satisfaction Problem (WCSP). We discuss how the WCSP model with a memory effect can be used to study hysteresis combinatorially; and in this context, we also discuss how the memory effect is related to an effective temperature parameter. Turning to more complex variants of the Ising model, we show that the introduction of long-range dipole interactions leads to variations of the hysteresis curves and the introduction of three-spin interactions leads to the emergence of meta-stable plateau states. We also show how to apply the Discrete Fourier Transform for the analysis of such phase transitions in the Ising model induced by three-spin interactions.