Continuous Phase Transition of the Fully Frustrated 3D XY Model with a Magnetic Field in the [111] Direction

We study the fully frustrated three-dimensional XY model on a simple cubic lattice. This model describes a 3D array of superconducting grains in an applied magnetic field ${\bf H}=(\Phi_{0}/a^{2})(1/2,1/2,1/2)$. Using standard Metropolis Monte Carlo simulations with periodic boundary conditions, we obtain the internal energy $U$, the specific heat $C_{V}$, and the helicity modulus $\gamma$ of our system. Our results support the conclusion that our system has a continuous phase transition between two liquid-like phases. Disorder in the low-temperature phase is suggested by the behavior of the vortex density-density correlation function at a very low temperature, $T=0.01J/k_{\mathrm{B}}$. By contrast, previous results for ${\bf H}=(\Phi_{0}/a^{2})(1/3,1/3,1/3)$ indicate a first-order phase transition. Mean-field theory suggests a possible explanation for the liquid-like low-temperature phase: there are four degenerate unstable modes at the mean-field transition temperature $T_{c}^{\mathrm{MF}}$. We also use finite-size scaling and two renormalization group methods to determine the critical exponents $\alpha$, $v$, and $\nu$ for $C_{V}$, $\gamma$, and the correlation length $\xi$. We compare our values of these critical exponents with those for other phase transitions.