Phase transtions in frustrated two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>models

Abstract

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 $\ensuremath{\Upsilon}$ jumps to zero with a value $\frac{\ensuremath{\Upsilon}}{{k}_{B}T}\ensuremath{\gtrsim}\frac{2}{\ensuremath{\pi}}$ at a $T\ensuremath{\lesssim}{T}_{I}$. The application of frustrated $\mathrm{XY}$ models to the behavior of coupled Josephson junction arrays is discussed.