Event-chain Monte Carlo simulations of liquid crystalline phase transitions of hard triangles

Abstract We extend the rejection-free event-chain Monte-Carlo approach to a liquid crystal system consisting of infinitely thin hard triangles. This triangle liquid crystal behaves very similar to hard circular platelets, which are an important model system for discotic liquid crystals. We investigate the isotropic-nematic phase transition of the triangle liquid crystal in detail measuring orientational order parameter, susceptibility, and equation of state. Our results suggest that the transition is discontinuous. In the event-chain Monte-Carlo simulation, we treat the three vertices of triangles as relevant degrees of freedom and derive lifting probabilities that guarantee maximal global balance of the algorithm. We also present a novel approach to derive the lifting probabilities from diffusional splitting probabilities on the hard object. We achieve considerable performance gains as compared to standard local Monte-Carlo techniques, which we substantiate by comparison of auto-correlation times. With the application to triangle liquid crystals, we present the first event-chain Monte-Carlo simulation of surface-like objects, which widens the applicability of the event-chain Monte-Carlo technique considerably. The lifting rules that we derive for isolated triangles will also be applicable to extended triangulated surfaces.