Liquid Crystals and the Heilmann-Lieb model

VirginiaTech, Virginia, USA

March 21, 2018

In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb.

Slides

PDF:

• Jauslin_VAtech_2018.pdf

• tarball: 18vatech-1.0.tar.gz
• git repository: 18vatech-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