Crossover in theXYmodel from three to two dimensions

We study the crossover between two- and three-dimensional behaviors of the Villain form of the XY spin model on a three-dimensional lattice with anisotropic couplings J₁=J₂=J, J₃={α}J (0{≤}{α}{≤}1). The {α} dependence of various quantities is examined by means of duality transformations, Migdal renormalization group, and Monte Carlo simulations. For the specific heat, a crossover into the Kosterlitz-Thouless behavior takes place around {α}{}0.2, which corresponds to αcos{}0.015 in the cosine form of the XY model. Some implications for models of high-Tc superconductivity are discussed.