Mathematical Physics Seminar
Emergence of a nematic phase in a system of hard plates in three dimensions with discrete orientations
Location: Hill 705
Date & time: Thursday, 22 September 2016 at 2:00PM - 2:11PM
Ian Jauslin , University of Rome :We consider a system of hard parallelepipedes, which we call plates, of size 1 by k^a by k in which a is larger than 5~6 and no larger than 1. Each plate is in one of six orthogonal allowed orientations. We prove that, when the density of plates is sufficiently larger than k^(2-5a) and sufficiently smaller than k^(3-a), 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.