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An old result by Shearer relates the Lov\'asz Local Lemma with the independent set polynomial on graphs, and consequently, as observed by Scott and Sokal, with the partition function of the hard core lattice gas on graphs.
Ruelle, D.: Statistical mechanics: Rigorous results. W. A. Benjamin, Inc., New York-Amsterdam (1969)
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Erdös, P. and Lovász, L.: Problems and results on 3-chromatic hypergraphs and some related questions, in Infinite and finite sets. Vol. II, Colloq. Math. Soc. Janos Bolyai, Vol. 10, pp. 609-627. North-Holland, Amsterdam, (1975)
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Shearer, J. B.:On a problem of Spencer. Combinatorica
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Erdös, P. and Spencer, J.: Lopsided Lovász local lemma and Latin transversal, Discrete Appl. Math
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Dobrushin , R. L.: Perturbation methods of the theory of Gibbsian fields. in P. Bernard(editor). Lectures on Probability Theory and Statistics, Ecole d’Et�de Probabilit� de Saint-Flour XXIV - 1994. Lectures notes in Mathematics 1648, 1-66. Springer-Verlag, Berlin, (1996)
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Bollobás, B.: Random Graphs. Second Edition, Cambridge University Press, Cambridge, (2001)
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Haxell, P. E., A note on vertex list colouring. Combin. Probab. Comput
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Scott, A.; Sokal, A.: The repulsive lattice gas, the independent-set polynomial, and the Lovász local lemma. J. Stat. Phys
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Fernandez, R.; Procacci A.: Cluster expansion for abstract polymer models.New bounds from an old approach. Communications in Mathematical Physics
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Alon, N. and Spencer, J.: The Probabilistic Method. Third Edition. New York, Wiley-Interscience, (2008)
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