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Crystalline ordering and large fugacity expansion for hard core lattice particles

Ian Jauslin, Joel L. Lebowitz

2017

Abstract

Using an extension of Pirogov-Sinai theory we prove phase transitions, corresponding to sublattice orderings, for a general class of hard core lattice particle systems with a finite number of close packed configurations. These include many cases for which such transitions have been proven. The proof also shows that, for these systems, the Gaunt-Fisher expansion of the pressure in powers of the inverse fugacity (aside from an explicit logarithmic term) has a nonzero radius of convergence.

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PDF:

• Jauslin_Lebowitz_2017.pdf

LaTeX source:

• tarball: 17jl-0.1.tar.gz
• git repository: 17jl-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).

Other releases

• arXiv preprint: arXiv:1705.02032.
• peer reviewed version, published in Journal of Physical Chemistry B, volume 122, number 13, pp 3266-3271 doi:10.1021/acs.jpcb.7b08977.

Talks

This work has been presented at the following conferences:

• [UMSM20]: Crystalline ordering in hard-core lattice particle systems
  Uniqueness methods in Statistical Mechanics, online, Dec 15 2020
  pdf, source


• [HaHU20]: Crystalline ordering in hard-core lattice particle systems
  Harvard University, Cambridge, Massachusetts, USA, Aug 05 2020
  pdf, source


• [Pr18]: Crystalline ordering and large-fugacity expansion for hard-core lattice particle systems
  Princeton University, New Jersey, USA, Feb 06 2018
  pdf, source


• [IASm17]: High density phases of hard-core lattice particle systems
  Member seminar, Institute for Advanced Study, Princeton, New Jersey, USA, Oct 30 2017
  video, pdf, source


• [Rut17]: High density phases of hard-core lattice particle systems
  Rutgers University, Princeton, New Jersey, USA, Oct 26 2017
  pdf, source


• [GLaMP17]: Crystalline ordering and large-fugacity expansion for hard-core lattice particle systems
  Great Lakes Mathematical Physics Meeting 2017, East Lansing, Michigan, USA, Jun 24 2017
  pdf, source