Abstract

The high-density hard-core configuration model has attracted attention for quite a long time. The first rigorous results about the phase transition on a lattice with a nearest-neighbor exclusion where published by Dobrushin in 1968. In 1979, Baxter calculated the free energy and specified the critical point on a triangular lattice with a nearest-neighbor exclusion; in 1980 Andrews gave a rigorous proof of Baxter’s calculation with the help of Ramanujan’s identities. We analyze the hard-core model on a triangular lattice and identify the extreme Gibbs measures (pure phases) for high densities. Depending on arithmtic properties of the hard-core diameter $D$, the number of pure phases equals either $D^{2$ or $2D}2$. A classification of possible cases can be given in terms of Eisenstein primes.

If the time allows, I will mention 3D analogs of some of these results.

This is a joint work with A Mazel and I Stuhl. No special knowledge will be assumed from the audience.