Monte Carlo study of the Villain version of the fully frustrated XY model

The fully frustrated XY model with Villain interaction on a square lattice is studied by means of Monte Carlo simulations. On the basis of the universal jump condition it is argued that there are two distinct transitions in the model, corresponding to the loss of XY order and Z₂ order, respectively. The Kosterlitz-Thouless (KT) transition is analyzed by finite-size scaling of the helicity modulus at lattices of size L=32 through 128, giving TKT{≈}0.8108(1). The vorticity-vorticity correlation function is used to determine two different characteristic lengths, the Z₂ correlation length {ξ}, and the screening length {λ}, associated with the KT transition and free vortices. The temperature dependence of {ξ} is examined in order to determine Tc and the correlation length exponent, {ν}. The exponent is found to be consistent with the two-dimensional (2D) Ising value, {ν}=1, and the obtained critical temperature is Tc=0.8225(5). The determinations of both {ξ} and {ν} are done carefully, first applying the techniques to the 2D Ising model, which serves as a convenient testing ground.