Algorithms for the ferromagnetic Potts model on expanders
2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)(2022)
摘要
We give algorithms for approximating the partition function of the ferromagnetic Potts model on d-regular expanding graphs. We require much weaker expansion than in previous works; for example, the expansion exhibited by the hypercube suffices. The main improvements come from a significantly sharper analysis of standard polymer models, using extremal graph theory and applications of Karger’s algorithm to counting cuts that may be of independent interest. It is #BIS-hard to approximate the partition function at low temperatures on bounded-degree graphs, so our algorithm can be seen as evidence that hard instances of #BIS are rare. We believe that these methods can shed more light on other important problems such as sub-exponential algorithms for approximate counting problems.
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关键词
Potts model,random cluster model,approximate counting,approximate sampling,expander graphs
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