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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)
Recent work has made substantial progress in understanding the transitions of random constraint satisfaction problems (CSPs). In particular, for several of these models, the exact satisfiability threshold has been rigorously determined, confirming predictions from the statistical physics literature. Here we revisit one of these models, random regular(More)
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