Nematic liquid crystal phase in a system of interacting dimers

Mathematical Challenges in Quantum Mechanics 2018, Rome, Italy

February 23, 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_MCQM_2018

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