Restricted orientation “liquid crystal” in two dimensions: Isotropic-nematic transition or liquid-gas one(?)

Institute of Theoretical Physics, Georg-August-Universität Göttingen - Friedrich-Hund-Platz 1, 37077 Göttingen, Germany, EU

Received: 10 December 2008
Accepted: 16 February 2009

Abstract

We present Monte Carlo simulation results of the two-dimensional Zwanzig fluid, which consists of hard line segments which may orient either horizontally or vertically. At a certain critical fugacity, we observe a phase transition with a two-dimensional Ising critical point. Above the transition point, the system is in an ordered state, with the majority of particles being either horizontally or vertically aligned. In contrast to previous work, we identify the transition as being of the liquid-gas type, as opposed to isotropic-to-nematic one. This interpretation naturally accounts for the observed Ising critical behavior. Furthermore, when the Zwanzig fluid is extended to more allowed particle orientations, we argue that in some cases the symmetry of a q-state Potts model with arises. This observation is used to interpret a number of previous results.