Crystalline ordering in hardcore lattice particle systems
Uniqueness methods in Statistical Mechanics, online
December 15, 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
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 tarball: 20umsm1.0.tar.gz
 git repository: 20umsmgit (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]: 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 
[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