Two phase transitions in the fully frustrated $XY$ model

TL;DR

This paper investigates the fully frustrated XY model on a square lattice, revealing two distinct phase transitions: a Kosterlitz-Thouless transition at approximately 0.446 and an Ising transition at about 0.452, clarified through Monte Carlo simulations.

Contribution

It demonstrates the existence of two separate phase transitions in the model and explains previous non-Ising exponents as finite size effects related to the Kosterlitz-Thouless transition.

Findings

Identification of two phase transitions at specific temperatures

Explanation of non-Ising exponents as finite size effects

Clarification of the relationship between Kosterlitz-Thouless and Ising transitions

Abstract

The fully frustrated $XY$ model on a square lattice is studied by means of Monte Carlo simulations. A Kosterlitz-Thouless transition is found at $T_{\rm KT} \approx 0.446$, followed by an ordinary Ising transition at a slightly higher temperature, $T_c \approx 0.452$. The non-Ising exponents reported by others, are explained as a failure of finite size scaling due to the screening length associated with the nearby Kosterlitz-Thouless transition.