Monte Carlo simulation of an strongly coupled XY model in three dimensions

TL;DR

This study uses advanced Monte Carlo simulations to explore a coupled XY model in three dimensions, revealing a tricritical point that explains anomalous critical behavior observed in liquid crystal phase transitions.

Contribution

The paper provides the first detailed Monte Carlo analysis of the 3D coupled XY model, identifying a tricritical point that clarifies experimental anomalies in liquid crystal phase transitions.

Findings

Existence of a tricritical point in the model.

Verification that large specific heat anomalies are due to proximity to the tricritical point.

Simulation results align with experimental observations of non-XY critical exponents.

Abstract

Many experimental studies, over the past two decades, have constantly reported a novel critical behavior for the transition from Smectic-A phase of liquid crystals to Hexatic-B phase with non-XY critical exponents. However according to symmetry arguments this transition must belong to XY universality class. Using an optimized Monte Carlo simulation technique based on multi-histogram method, we have investigated phase diagram of a coupled XY model, proposed by Bruinsma and Aeppli (PRL {\bf 48}, 1625 (1982)), in three dimensions. The simulation results demonstrate the existence of a tricritical point for this model, in which two different orderings are established simultaneously. This result verifies the accepted idea the large specific heat anomaly exponent observed for SmA-HexB transition could be due to the occurrence of this transition in the vicinity of a tricritical point