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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 consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T , and study the existence of the free energy density φ, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to… (More)

We establish the satisfiability threshold for random k-SAT for all k ≥ k<sub>0</sub>. That is, there exists a limiting density α<sub>s</sub>(k) such that a random k-SAT formula of clause density α is with high probability satisfiable for α < α<sub>s</sub>, and unsatisfiable for α > α<sub>s</sub>. The satisfiability… (More)

We consider the random regular <i>k</i>-nae-sat problem with <i>n</i> variables each appearing in exactly <i>d</i> clauses. For all <i>k</i> exceeding an absolute constant <i>k</i><sub>0</sub>, we establish explicitly the satisfiability threshold <i>d</i><sub>*</sub> ∈ <i>d</i><sub>*</sub>(<i>k</i>). We prove that for <i>d</i> <… (More)

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