A Monte Carlo analysis of the phase transitions in the 2D, $J_1-J_2$ XY model

TL;DR

This paper investigates the phase transitions in the 2D $J_1-J_2$ XY model, revealing two distinct transitions and large finite size effects that clarify previous inconsistent findings.

Contribution

The study provides a detailed Monte Carlo analysis showing two separate phase transitions and introduces a new method to analyze the Kosterlitz-Thouless transition without relying on the helicity jump.

Findings

Identification of two close but separate phase transitions.

Discovery of non-Ising universality class for one transition.

Evidence of large finite size effects in the model.

Abstract

We consider the 2D $J_1-J_2$ classical XY model on a square lattice. In the frustrated phase corresponding to $J_2>J_1/2$, an Ising like order parameter emerges by an ``order due to disorder'' effect. This leads to a discrete $Z_2$ symmetry plus the U(1) global one. Using a powerful algorithm we show that the system undergoes two transitions at different but still very close temperatures, one of Kosterlitz-Thouless (KT) type and another one which does not belong to the expected Ising universality class. A new analysis of the KT transition has been developed in order to avoid the use of the non-universal helicity jump and to allow the computation of the exponents without a precise determination of the critical temperature. Moreover, our huge number of data enables us to exhibit the existence of large finite size effects explaining the dispersed results found in the literature concerning the more studied frustrated 2D, XY models.