Y. Guan, A. Li, S. Koenig, S. Haas and S. Kumar. Hysteresis in Combinatorial Optimization Problems. In International FLAIRS Conference (FLAIRS), 2021.

Abstract: Hysteresis is a physical phenomenon reflected in macroscopic observables of materials that are subjected to external fields. For example, magnetic hysteresis is observed in ferromagnetic metals such as iron, nickel and cobalt in the presence of a changing external magnetic field. In this paper, we model hysteresis using combinatorial models of microscopic spin interactions, for which we invoke the top K solution framework for Ising models and their generalizations, called Weighted Constraint Satisfaction Problems (WCSPs). We show that the WCSP model with a simple 'memory effect' can be used to understand hysteresis combinatorially and from the perspective of statistical mechanics. In addition to the nearest neighbor interaction Ising model, the WCSP framework facilitates accurate simulations of long-range and k-body interactions between the spins.

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