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The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising model with arbitrary external field, it is np-hard to approximate the partition function or approximately sample from the(More)
We provide an explicit formula for the limiting free energy density (log-partition function divided by the number of vertices) for ferromagnetic Potts models on uniformly sparse graph sequences converging locally to the d-regular tree for d even, covering all temperature regimes. This formula coincides with the Bethe free energy functional evaluated at a(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract Let T be a rooted supercritical multi-type Galton–Watson (MGW) tree with types coming from a finite alphabet, conditioned to non-extinction. The λ-biased random walk (Xt) t≥0 on T is the nearest-neighbor random walk which, when at a vertex v with dv offspring, moves closer to the root with(More)
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