Liquid Crystals and the Heilmann-Lieb model
Liquid crystals are everywhere, and they do more for you than you might think. They tell you the weather, the time, and will kindly let you know that your connection to eduroam was rejected, and that you'll have to listen to the rest of the seminar. Indeed, most displays run on liquid crystals, from the small dials in digital wristwatches to large flat-screen televisions. In this paper, I will review some results pertaining to why (or, perhaps, how) liquid crystals exist in the first place. In particular, I will focus on a model introduced by Heilmann and Lieb in 1979, for which Lieb and I have recently proved the emergence of a nematic liquid crystal phase.
This paper is an informal discussion of the content of [JL17c].
- tarball: 18j-iamp-1.0.tar.gz
- git repository: 18j-iamp-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
- This article appears in the IAMP News Bulletin, April 2018.
[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)