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Ising Model Partition Function Computation as a Weighted Counting Problem

Shaan A. NagyRoger ParedesJeffrey M. DudekLeonardo Due\~nas-OsorioMoshe Y. Vardi
Dec 2022
摘要
While the Ising model remains essential to understand physical phenomena, itsnatural connection to combinatorial reasoning makes it also one of the bestmodels to probe complex systems in science and engineering. We bring acomputational lens to the study of Ising models, where our computer-scienceperspective is two-fold: On the one hand, we consider the computationalcomplexity of the Ising partition-function problem, or #Ising, and relate it tothe logic-based counting of constraint-satisfaction problems, or #CSP. We showthat known dichotomy results for #CSP give an easy proof of the hardness of#Ising and provide new intuition on where the difficulty of #Ising comes from.On the other hand, we also show that #Ising can be reduced to Weighted ModelCounting (WMC). This enables us to take off-the-shelf model counters and applythem to #Ising. We show that this WMC approach outperforms state-of-the-artspecialized tools for #Ising, thereby expanding the range of solvable problemsin computational physics.
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