Crossover from BKT to first-order transition induced by higher-order terms in 2D XY models

We study phase transitions in XY models, generalized by inclusion of n higher-order pairwise interactions of equal strength, by Monte Carlo simulation. It is found that by adding new terms the Berezinskii-Kosterlitz-Thouless (BKT) transition, observed in the standard XY model, gradually changes to the first-order phase transition. We determine the critical number of terms for which the first-order transition appears as $n_c=6$. It is also found that for $n=5$ the transition is pseudo-first-order but it becomes true first-order if the couplings are allowed to increase. In general, a more rapid increase of the coupling intensity supports the first-order transition, however, a too fast increase may result in splitting of the single transition to multiple transitions. Consequently, the minimal number of the terms required for the change of the BKT phase transition to first order in the present model with arbitrary couplings is estimated to be $2<n_c\le 5$.