DIMENSIONAL CROSSOVER IN THE XY-MODEL

We use the single-cluster Monte Carlo algorithm to simulate the periodic Gaussian XY model on L2 x N lattices of film geometry (L >> N) with up to N = 16 layers, imposing free boundary conditions at the bottom and top layer. Based on measurements of the specific heat, the spin-spin correlation function and the susceptibility in the high-temperature phase we study the crossover from three- to two-dimensional behaviour as criticality is approached. For the transition temperatures, determined from Kosterlitz-Thouless fits to the correlation length and susceptibility, we observe a pronounced scaling behaviour with N, but find an associated critical exponent that deviates from theoretical expectations. More qualitatively, we further investigate the shapes and distribution of vortex loops in the crossover region.