Phase transition of a two-dimensional generalized XY model

We study a 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, a regular KT transition and 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(KT).