High density phases of hardcore 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 hardcore 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:
LaTeX source:
 tarball: 17iasmember1.0.tar.gz
 git repository: 17iasmembergit (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 32663271)
pdf, source 
[JL17b]: Highfugacity expansion, LeeYang zeros and orderdisorder transitions in hardcore lattice systems
Ian Jauslin, Joel L. Lebowitz, 2017
(published in Communications in Mathematical Physics, volume 364, issue 2, pp 655–682)
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 9551002)
pdf, source