  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 ${\bf H} = (\Phi_0/a^2)(1/2,1/2,1/2)$. We find that the
model has a continuous phase transition with critical temperature $T_c = 0.681
J/k_B$, 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.
