Georgia Institute of Technology College of Sciences

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.