Continuous phase transition of a fully frustrated XY model in three dimensions

Abstract

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 ${\bf H} = (Φ_0/a^2)(1/2,1/2,1/2)$. 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 $α/ν= 0.87 \pm 0.01$, $v/ν= 0.82 \pm 0.01$, and $ν= 0.72 \pm 0.07$, where $α$, $v$, and $ν$ 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.