First-order and Berezinskii-Kosterlitz-Thouless phase transitions in two-dimensional generalized XY models

Besides the Berezinskii-Kosterlitz-Thouless phase transition, the two-dimensional generalized XY model, identified by a generalization parameter q (as proposed by Romano and Zagrebnov), can also support a first-order phase transition, starting from a critical value q(c). However, the value of q(c) at which this transition takes place is unknown. In this paper, we take two approaches to accurately determine the critical parameter q(c). Furthermore, we show that the model is characterized by three distinct regions concerning both first-order and BerezinskiiKosterlitz-Thouless phase transitions. Finally, the underlying mechanism governing such transitions is presented, along with an estimation of the critical temperatures.