A criterion for crystallization in hard-core lattice particle systems
University of Roma Tre, Rome, Italy
June 20, 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 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.
Slides
PDF:
LaTeX source:
- tarball: 24romatre-1.0.tar.gz
References
This presentation is based on
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[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 -
[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 -
[HJ24]: High-fugacity expansion and crystallization in non-sliding hard-core lattice particle models without a tiling constraint
Qidong He, Ian Jauslin, 2024
pdf, source