Dimensional crossover in the XY model

Wolfhard Janke E, Klaus Nather

Wolfhard Janke E, Tetsuo Matsui

H. G. Vaidya, Craig A. Tracy

Wolfhard Janke E, Tetsuo Matsui

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 ${\mathit{J}}_{1}$=${\mathit{J}}_{2}$=J, ${\mathit{J}}_{3}$=\ensuremath{\alpha}J (0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}1). The \ensuremath{\alpha} 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 \ensuremath{\alpha}\ensuremath{\simeq}0.2, which corresponds to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{cos}}$\ensuremath{\simeq}0.015 in the cosine form of the XY model. Some implications for models of high-${\mathit{T}}_{\mathit{c}}$ superconductivity are discussed.

Ivan S Popov, Anna P Popova, Pavel Vladimirovich Prudnikov

Abstract The study of critical properties and size transition in a diluted layered XY-model was carried out for the first time. The dimensional dependence of the temperature T BKT(p, N) of the Berezinskii-Kosterlitz-Thouless phase transition on the system thickness N is obtained for a diluted layered XY-model for a wide range of spin concentrations p. The temperature T, concentration p, and dimensional N dependencies of the vortex density v(p, N, T) in a layered XY-model are obtained.

Francesco Fucito