Crystalline ordering in hard-core lattice particle systems
Harvard University, Cambridge, Massachusetts, USA
August 5, 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:
LaTeX source:
- tarball: 20harvard-hu-1.0.tar.gz
- git repository: 20harvard-hu-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
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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