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

[摘要] 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 Z(2) 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 T(KT)approximate to 0.8108(1). The vorticity-vorticity correlation function is used to determine two different characteristic lengths, the Z(2) correlation length xi, and the screening length lambda, associated with the KT transition and free vortices. The temperature dependence of xi is examined in order to determine T, and the correlation length exponent, nu. The exponent is found to be consistent with the two-dimensional (2D) Ising value, nu=1, and the obtained critical temperature is T-c=0.8225(5). The determinations of both xi and nu are done carefully, first applying the techniques to the 2D Ising model, which serves as a convenient testing ground.

[关键词] CONSISTENT BOUNDARY-CONDITIONS;COULOMB-GAS REPRESENTATION;PHASE-TRANSITIONS;SUPERFLUID DENSITY;CRITICAL EXPONENTS;CRITICAL-BEHAVIOR;SQUARE-LATTICE;2 DIMENSIONS;SPIN SYSTEMS;ISING-MODEL