6533b835fe1ef96bd129eabf

RESEARCH PRODUCT

Monte Carlo simulation of dimensional crossover in the XY model.

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We report Monte Carlo simulations of Villain's periodic Gaussian XY model on ${\mathit{L}}^{2}$\ifmmode\times\else\texttimes\fi{}N lattices of film geometry (L\ensuremath{\gg}N) with up to N=16 layers, employing the single-cluster update algorithm combined with improved estimators for measurements. The boundary conditions are periodic within each layer and free at the bottom and top layer. Based on data for 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 behavior as criticality is approached. For the transition temperatures, determined from Kosterlitz-Thouless fits to the correlation length and susceptibility, we observe a pronounced scaling behavior with N. The associated critical exponent, however, deviates from theoretical expectations. More qualitatively, we further discuss the distribution and shapes of vortex loops in the crossover region.