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

TL;DR

This study uses Monte Carlo simulations to show that adding higher-order interactions to 2D XY models causes the BKT transition to become a first-order transition at a critical number of terms, with detailed dependence on coupling strength.

Contribution

It identifies the critical number of higher-order terms needed to induce a first-order transition in generalized 2D XY models.

Findings

BKT transition changes to first-order at n_c=6.

For n=5, the transition is pseudo-first-order, becoming true first-order with increased couplings.

Rapid coupling increase supports first-order transition but may cause multiple transitions.

Abstract

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 $2 < n_c \leq 5$.