Crystalline ordering in hard-core lattice particle systems

Uniqueness methods in Statistical Mechanics, online

December 15, 2020

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 accomplish 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.

Slides

PDF:

• Jauslin_UMSM_2020.pdf

• tarball: 20umsm-1.0.tar.gz
• git repository: 20umsm-git (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).

References

This presentation is based on

• [JL17b]: High-fugacity expansion, Lee-Yang zeros and order-disorder transitions in hard-core lattice systems
  Ian Jauslin, Joel L. Lebowitz, 2017
  (published in Communications in Mathematical Physics, volume 364, issue 2, pp 655–682, 2018)
  pdf, source


• [JL17]: Crystalline ordering and large fugacity expansion for hard core lattice particles
  Ian Jauslin, Joel L. Lebowitz, 2017
  (published in Journal of Physical Chemistry B, volume 122, number 13, pp 3266-3271, 2017)
  pdf, source