Abstract: 

I will present a class of hard-core lattice particle systems which exhibit a crystalline phase at high densities. The key ingredient of the proof is to show that the Gaunt-Fisher high-fugacity expansion is convergent for such models, which we acomplish using methods from Pirogov-Sinai theory. Crystallization can then be proved by studying the lower order terms of the expansion and bounding the remainder. This is joint work with Joel L. Lebowitz.