High density phases of hard-core lattice particle systems

Member seminar, Institute for Advanced Study, Princeton, New Jersey, USA

September 30, 2017

In this talk, I will discuss the behavior of hard-core lattice particle systems at high fugacities. I will first present a collection of models in which the high fugacity phase can be understood by expanding in powers of the inverse of the fugacity. I will then discuss a model in which this expansion diverges, but which can still be solved by expanding in other high fugacity variables. This model is an interacting dimer model, introduced by O.Heilmann and E.H.Lieb in 1979 as an example of a nematic liquid crystal. Heilmann and Lieb proved that the dimers spontaneously align, and conjectured that they do not exhibit long range positional order. I will present a recent proof of this conjecture.

Video

The video of this talk is available here.

Slides

PDF:

• Jauslin_IAS-member_2017

• tarball: 17ias-member-1.0.tar.gz
• git repository: 17ias-member-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

• [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


• [JL17c]: Nematic liquid crystal phase in a system of interacting dimers and monomers
  Ian Jauslin, Elliott H. Lieb, 2017
  (published in Communications in Mathematical Physics, volume 363, issue 3, pp 955-1002, 2018)
  pdf, source