Algorithms for the ferromagnetic Potts model on expanders [article]

Charlie Carlson, Ewan Davies, Nicolas Fraiman, Alexandra Kolla, Aditya Potukuchi, Corrine Yap
2022 arXiv   pre-print
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
more » ... ion 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.
arXiv:2204.01923v2 fatcat:knakkirdifbt3etwsjhp36hanu