Fast Algorithms for General Spin Systems on Bipartite Expanders

A spin system is a framework in which the vertices of graph are assigned spins from finite set. The interactions between neighbouring give rise to weights, so assignment can also be viewed as weighted homomorphism. problem approximating partition function (the aggregate weight assignments) or sampling resulting probability distribution typically intractable for general graphs. In this work, we consider arbitrary systems on bipartite expander Δ-regular graphs, including canonical class random We develop fast approximate and counting algorithms whenever degree spectral gap sufficiently large. Roughly, guarantees that so-called low-temperature regime. Our approach generalises techniques Jenssen et al. Chen by showing typical configurations expanders correspond “bicliques” system; then, using suitable polymer models, show how sample such Õ( n 2 ) time, where size graph.