We simulate, by the Monte Carlo method, a fully frustrated antiferromagnet of classical XY spins on a square lattice in two dimensions, with nearest- and second-nearest-neighbor interactions (${\mathit{J}}_1$ and ${\mathit{J}}_2$) for ${\mathit{J}}_1$=${\mathit{J}}_2$. Rotations of all spins on one sublattice with respect to all spins on the other sublattice leave the ground-state energy invariant. We first check, numerically, that the temperature does, as previously predicted, introduce an anisotropy that gives rise to an Ising-like broken symmetry in the ordered state at T>0. Our results are consistent with one critical temperature, where both magnetization fluctuations and fluctuations of the appropriate Ising-like order parameter diverge. Critical fluctuations of the magnetization seem to cross over from a Kosterlitz-Thouless-type behavior to ξ∼${\mathit{t}}^{\mathrm{-}\nu }$ (ν≊1) as ξ becomes large enough (ξ>10 lattice units) for anisotropy effects to become dominant. Values of several critical indices are obtained. In addition, critical effects produced by small amounts of impurities are studied. We find that the reduced crossover temperature into the impurity-dominated regime is given by t∼δ${\mathit{n}}^{2/\mathrm{\phi }}$,φ≊1.7, where δn is the impurity concentration. This result differs sharply from the predictions of the Harris criterion.

• Received 24 June 1991

DOI:https://doi.org/10.1103/PhysRevB.44.10057