High-fugacity expansion and crystallization in non-sliding hard-core lattice particle models without a tiling constraint
2024
Abstract
In this paper, we prove the existence of a crystallization transition for a family of hard-core particle models on periodic graphs in arbitrary dimensions. We establish a criterion under which crystallization occurs at sufficiently high densities. The criterion is more general than that in [Jauslin, Lebowitz, Comm. Math. Phys. 364:2, 2018], as it allows models in which particles do not tile the space in the close-packing configurations, such as discrete hard-disk models. To prove crystallization, we prove that the pressure is analytic in the inverse of the fugacity for large enough complex fugacities, using Pirogov-Sinai theory. One of the main tools used for this result is the definition of a local density, based on a discrete generalization of Voronoi cells. We illustrate the criterion by proving that it applies to two examples: staircase models and the radius 2.5 hard-disk model on the square lattice.
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Changelog
- v0.0.1:
- fix: Typos, and improved readability
- change: Colors of figures for better black and white printing and color blind viewing
Other releases
- arXiv preprint: arXiv:2402.02615.
Related articles
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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
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