  The aim of this paper is to illustrate that generalized two-dimensional XY
models (proposed by Romano and Zagrebnov) may also support a first-order phase
transition. Two approaches are employed to accurately determine the critical
parameter $q$ at which such a transition takes place. Furthermore, we show that
the model is characterized by three distinct regions concerning both
first-order and Berezinskii-Kosterlitz-Thouless phase transitions. Finally, the
underlying mechanisms governing such transitions are presented, along with an
estimation of the critical temperatures.
