CROSSOVER IN THE XY MODEL FROM 3 TO 2 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=J (01). The 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 0.2, which corresponds to 0.015 in the cosine form of the XY model. Some implications for models of high-Tc superconductivity are discussed. © 1990 The American Physical Society.