Plate-nematic phase in three dimensions

TL;DR

This paper proves the existence of a uni-axial nematic phase in a three-dimensional system of anisotropic plates with finite orientations, characterized by long-range orientational order without translational order, using a rigorous contour model approach.

Contribution

It introduces a rigorous proof of the nematic phase in 3D plate systems with hard core interactions and finite orientations, employing Pirogov-Sinai methods.

Findings

Existence of a uni-axial nematic phase at certain densities.

Long-range orientational order without translational order.

Rigorous control of the contour model via coarse graining.

Abstract

We consider a system of anisotropic plates in the three-dimensional continuum, interacting via purely hard core interactions. We assume that the particles have a finite number of allowed orientations. In a suitable range of densities, we prove the existence of a uni-axial nematic phase, characterized by long range orientational order (the minor axes are aligned parallel to each other, while the major axes are not) and no translational order. The proof is based on a coarse graining procedure, which allows us to map the plate model into a contour model, and in a rigorous control of the resulting contour theory, via Pirogov-Sinai methods.