Crystalline ordering in hardcore lattice particle systems
Harvard University, Cambridge, Massachusetts, USA
August 5, 2020
I will present a class of hardcore lattice particle systems which exhibit a crystalline phase at high densities. The key ingredient of the proof is to show that the GauntFisher highfugacity expansion is convergent for such models, which we accomplish using methods from PirogovSinai 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:
LaTeX source:
 tarball: 20harvardhu1.0.tar.gz
 git repository: 20harvardhugit (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

[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 32663271)
pdf, source 
[JL17b]: Highfugacity expansion, LeeYang zeros and orderdisorder transitions in hardcore lattice systems
Ian Jauslin, Joel L. Lebowitz, 2017
(published in Communications in Mathematical Physics, volume 364, issue 2, pp 655–682)
pdf, source