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Sphere-packings on lattices in mathematical physics

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Dense-packing problems on two and three dimensional lattices will be discussed, and their role will be shown in the analysis of the phase diagram of the hard-core model. Namely, high-density pure phases/extreme Gibbs distributions of the model are generated by certain ground states – in accordance with the Pirogov-Sinai theory – which are dense-packings for this model in the high-density regime.

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