Ian Jauslin

## Emergence of a nematic phase in a system of hard plates

Rutgers University, USA

### 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 $$k^{2-5\alpha}$$ 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 two-scale cluster expansion, and uses ideas from the Pirogov-Sinai construction.

Joint work with Margherita Disertori and Alessandro Giuliani

### Slides

PDF:

LaTeX source:
• tarball: 16rutgers-1.0.tar.gz
• git repository: 16rutgers-git (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).

### References

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