Liquid crystals and the Heilmann-Lieb model

University of British Columbia, Vancouver, British Columbia, Canada

January 10, 2020

A liquid crystal is a phase of matter in which order and disorder coexist: for some degrees of freedom, there is order, whereas for others, disorder. Such materials were discovered in the late XIXth century, but it took over a century to understand, from microscopic models, how such phases form. In 1979, O. Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of such a liquid crystal phase. In this setting, this amounts to showing that dimers spontaneously align, but do not fully crystallize: there is no translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. In this talk, I will discuss a recent proof of this conjecture, that is, a proof of the emergence of a liquid crystal phase in the Heilmann-Lieb model. This is joint work with E.H. Lieb.

Slides

PDF:

• Jauslin_UBC_colloquium_2020.pdf

• tarball: 20ubc-colloquium-1.0.tar.gz
• git repository: 20ubc-colloquium-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

• [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