Competing nematic interactions in a generalized XY model in two and three dimensions

TL;DR

This paper investigates a generalized XY model with nematic interactions in two and three dimensions, revealing complex phase diagrams with multiple types of phase transitions, including BKT and infinite order transitions, especially for the case q=8.

Contribution

It introduces a comprehensive numerical analysis of a generalized XY model with nematic interactions, highlighting new intermediate phases and transition types for q=8.

Findings

Multiple phase transitions including BKT and infinite order transitions.

Presence of intermediate, competition-driven phases absent in lower q cases.

Vortex decoupling is not sufficient to identify BKT transitions.

Abstract

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of $2\pi/q$ between neighboring spins. We focus here on the $q=8$ case (while presenting new results for other values of $q$ as well) whose phase diagram is much richer than the well known $q=2$ case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in $q=2$, but also infinite order transitions involving intermediate, competition driven phases absent for $q=2$ and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a suficient condition for it to be of BKT type.