Multiple phase transitions in the $XY$ model with nematic-like couplings

TL;DR

This study uses Monte Carlo simulations to reveal that a 2D generalized XY model with nematic-like couplings undergoes three successive phase transitions, including Berezinskii-Kosterlitz-Thouless and Ising types, leading to multiple nematic and ferromagnetic phases.

Contribution

It demonstrates the existence of multiple phase transitions in a generalized XY model with nematic-like interactions, highlighting complex critical behavior not previously characterized.

Findings

Three successive phase transitions identified: BKT, then two Ising transitions.

Nematic-like phases characterized by specific spin angle alignments.

Ferromagnetic phase emerges at low temperatures without magnetic interactions.

Abstract

Critical behavior of the two-dimensional generalized $XY$ model involving solely nematic-like terms of the second, third and fourth orders is studied by Monte Carlo method. We find that such a system can undergo three successive phase transitions. At higher temperatures there is a phase transition of the Berezinskii-Kosterlitz-Thouless type to the $q=4$ nematic-like phase, followed by two more transitions of the Ising type to the $q=2$ nematic-like and ferromagnetic phases, respectively. The $q$ nematic-like phases are characterized by spin alignments with angles $2k\pi/q$, where $k \leq q$ is an integer. The ferromagnetic phase appears at low temperatures even without the presence of magnetic interactions owing to a synergic effect of the nematic-like terms.