Emergence of a nematic phase in a system of hard plates
Rutgers University, USA
September 22, 2016
Abstract
We consider a system of hard parallelepipedes, which we call plates, of size \(1\times k^\alpha \times k\) in which \(\frac56< \alpha \leqslant 1\). Each plate is in one of six orthogonal allowed orientations. We prove that, when the density of plates is sufficiently larger than \(k^{25\alpha}\) and sufficiently smaller than \(k^{3\alpha}\), the rotational symmetry of the system is broken, but its translational invariance is not. In other words, the system is in a nematic phase. The argument is based on a twoscale cluster expansion, and uses ideas from the PirogovSinai construction.
Joint work with Margherita Disertori and Alessandro Giuliani
Slides
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 tarball: 16rutgers1.0.tar.gz
 git repository: 16rutgersgit (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

[DGJ18]: Platenematic phase in three dimensions
Margherita Disertori, Alessandro Giuliani, Ian Jauslin, 2018
(published in Communications in Mathematical Physics, volume 373, issue 1, pp 327256, 2020)
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