Crystalline Ordering and Large Fugacity Expansion for Hard-Core Lattice Particles.

Using an extension of Pirogov-Sinai theory, we prove phase transitions, corresponding to sublattice orderings, for a general class of hard-core lattice particle systems with a finite number of perfect coverings. These include many cases for which such transitions have been proven. The proof also shows that for these systems the Gaunt-Fisher expansion of the pressure in powers of the inverse fugacity (aside from an explicit logarithmic term) has a nonzero radius of convergence.