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High-fugacity expansion, Lee-Yang zeros and order-disorder transitions in hard-core lattice systems

Ian Jauslin, Joel L. Lebowitz

2017

Abstract

We establish existence of order-disorder phase transitions for a class of "non-sliding" hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a finite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee-Yang zeros lie in an annulus with finite positive radii.

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PDF:

• Jauslin_Lebowitz_2017b.pdf

LaTeX source:

• tarball: 17jlB-0.2.1.tar.gz
• git repository: 17jlB-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:1708.01912.
• This paper is published in Communications in Mathematical Physics, Volume 364, Issue 2, pp 655–682, doi:10.1007/s00220-018-3269-7.

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