Phase transition of two-dimensional generalized XY model

TL;DR

This study uses Monte Carlo simulations to analyze the phase transition behavior of the two-dimensional generalized XY model, revealing a single Kosterlitz-Thouless transition across all parameter values, contrary to prior expectations.

Contribution

It demonstrates that the generalized XY model exhibits only one KT transition for all q values, challenging previous hypotheses of multiple transitions.

Findings

Single KT transition for all q values

Universality of KT transition scaling behaviors

Contradicts earlier speculation of multiple transitions

Abstract

We study the two-dimensional generalized XY model that depends on an integer $q$ by the Monte Carlo method. This model was recently proposed by Romano and Zagrebnov. We find a single Kosterlitz-Thouless (KT) transition for all values of $q$, in contrast with the previous speculation that there may be two transitions, one a regular KT transition and another a first-order transition at a higher temperature. We show the universality of the KT transitions by comparing the universal finite-size scaling behaviors at different values of $q$ without assuming a specific universal form in terms of the KT transition temperature $T_{\rm KT}$.