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We point out a close connection between the Moser-Tardos algorithmic versionof the Lov\'asz Local Lemma, a central tool in probabilistic combinatorics, andthe cluster expansion of the hard core lattice gas in statistical mechanics. Weshow that the notion of witness trees given by Moser and Tardos is essentiallycoincident with that of Penrose trees in the Cluster expansion scheme of thehard core gas. Such an identification implies that the Moser Tardos algorithmis successful in a polynomial time if the Cluster expansion converges.

Witness trees in the Moser-Tardos algorithmic Lov\'asz Local Lemma and Penrose trees in the hard core lattice gas