Thermal phase diagram of a model Hamiltonian for columnar phases of liquid crystals

TL;DR

This study explores the phase diagram of a coupled XY-Ising model relevant to liquid crystal columnar phases, revealing a phase with XY order and Ising disorder and suggesting a 2D-Ising universality class for the transitions.

Contribution

It provides a comprehensive analysis of the phase diagram using multiple methods, clarifying the universality class of the phase transitions in the model.

Findings

Phase diagram shows a phase with XY order and Ising disorder.

Transitions belong to the 2D-Ising universality class.

Results are consistent across mean-field, renormalization group, and Monte Carlo methods.

Abstract

We present the phase diagram and critical properties of a coupled $XY$-Ising model on a triangular lattice using the mean-field approximation, the Migdal-Kadanoff scheme of renormalization group and Monte-Carlo simulations. The topology of the phase diagram is similar for the three techniques, with the appearance of a phase with $XY$ order and Ising disorder. The results suggest a line of transitions belonging to the 2D-Ising universality class in contrast with previous data indicating a new universality class. This model is relevant to the columnar phases of discotic liquid crystals [such as hexa(hexylthio)triphenylene (HHTT)] in the limit of weak intercolumn coupling.