Ian Jauslin

A criterion for crystallization in hard-core 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 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.

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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

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