A criterion for crystallization in hard-core lattice particle systems

Ian Jauslin, Rutgers
Jadwin Hall A06

As is well known, many materials freeze at low temperatures. Microscopically,  this means that their molecules form a phase where there is long range order  in their positions. Despite their ubiquity, proving that these freezing  transitions occur in realistic microscopic models has been a significant  challenge, and it remains an open problem in continuum models at positive temperatures. In this talk, I will focus on lattice particle models, in which  the positions of particles are discrete, and discuss a general criterion under which crystallization can be proved to occur. The class of models that  the criterion applies to are those in which there is *no sliding*, that is, particles are largely locked in place when the density is large. The tool  used in the proof is Pirogov-Sinai theory and cluster expansions. I will present the criterion in its general formulation, and discuss some concrete  examples. This is joint work with Qidong He and Joel L. Lebowitz.