Two Phase Transitions in the Fully FrustratedXYModel

The fully frustrated $\mathrm{XY}$ model on a square lattice is studied by means of Monte Carlo simulations. A Kosterlitz-Thouless transition is found at $T_{\mathrm{KT}}\approx 0.446$, 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.