Ian Jauslin
Rutgers University, USA
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
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