We have used Monte Carlo simulations, combined with finite-size scaling and two different real-space renormalization group approaches, to study a fully frustrated three-dimensional $XY$ model on a simple cubic lattice. This model corresponds to a lattice of Josephson-coupled superconducting grains in an applied magnetic field $\mathbf{H}=({\Phi }_0∕a^2)(1∕2,1∕2,1∕2)$. We find that the model has a continuous phase transition with critical temperature $T_c=0.681J∕k_B$, where $J$ is the $XY$ coupling constant, and critical exponents $\alpha ∕\nu =0.87\pm 0.01$, $v∕\nu =0.82\pm 0.01$, and $\nu =0.72\pm 0.07$, where $\alpha$, $v$, and $\nu$ describe the critical behavior of the specific heat, helicity modulus, and correlation length. We briefly compare our results with other studies of this model, and with a mean-field approximation.

• Received 21 February 2006

DOI:https://doi.org/10.1103/PhysRevB.73.224504