Dimensional Crossover in Critical Behavior of Thin XY-films: Equilibrium and Non-equilibrium Properties

In the present work it is studied the dimensional crossover in the critical behavior of the thin XY-films. Increasing the thickness N of XY-film leads to a gradual transition from the Berezinskii-Kosterlitz-Thouless phase transition in the two-dimensional XY-model to the "ferromagnetic-paramagnetic" phase transition in the three-dimensional XY-model. It is investigated how phenomena associated with the topological phase disappears when film thickness N is increased. The main consideration is focused on the dependence of the spin stiffness ρ _s on the thickness N. In this work a generalization of Pokrovsky-Uimin equation for spin-wave approximation is introduced. The dynamical dependencies of thermodynamic values in non-equilibrium relaxation from low-temperature and high-temperature initial states are investigated. (paper)