A criterion for crystallization in hardcore lattice particle systems
Princeton University, New Jersey, USA
February 27, 2024
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 PirogovSinai 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.
Slides
PDF:
LaTeX source:
 tarball: 24princeton1.0.tar.gz
Visualizations
This presentation includes some visualizations of configurations, that can be viewed and manipulated using Jam. The configuration files are located in the tarball, under the directory 'figs/configurations.jam'.
References
This presentation is based on

[HJ24]: Highfugacity expansion and crystallization in nonsliding hardcore lattice particle models without a tiling constraint
Qidong He, Ian Jauslin, 2024
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, 2018)
pdf, source