Phase transtions in frustrated two-dimensionalXYmodels

We study the fully frustrated $\mathrm{XY}$ model on a square lattice with the use of Monte Carlo simulations. We find a phase transition at a finite temperature $T_I$ with the specific-heat data being consistent with a logarithmic divergence. The helicity modulus $\Upsilon$ jumps to zero with a value $\frac{\Upsilon }{k_{B}T}\gtrsim \frac{2}{\pi }$ at a $T\lesssim T_I$. The application of frustrated $\mathrm{XY}$ models to the behavior of coupled Josephson junction arrays is discussed.