A bound on the second biadjacency singular value alone certifies FPRAS counting and polynomial-time sampling for the hard-core model at every fugacity on Δ-regular bipartite graphs.
\# bis-hardness for 2-spin systems on bipartite bounded degree graphs in the tree non-uniqueness region
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The Hard-Core Model on Bipartite Spectral Expanders: Counting and Sampling at All Fugacities
A bound on the second biadjacency singular value alone certifies FPRAS counting and polynomial-time sampling for the hard-core model at every fugacity on Δ-regular bipartite graphs.