The Kosterlitz-Thouless transition in thin films: a Monte Carlo study of three-dimensional lattice models

We study the phase transition of thin films in the three-dimensional XY universality class. To this end, we perform a Monte Carlo study of the improved two-component phi(4) model, the improved dynamically diluted XY model and the standard XY model on the simple cubic lattice. We study films of a thickness up to L-0 = 32 lattice spacings. In the short direction of the lattice, free boundary conditions are employed. Using a finite size scaling (FSS) method, proposed recently, we determine the transition temperature with high accuracy. The effectively two-dimensional finite size scaling behaviour of the Binder cumulant U-4, the second-moment correlation length over the lattice size xi(2nd)/L, the ratio of the partition functions with anti-periodic and periodic boundary conditions Z(a)/Z(p) and the helicity modulus Gamma clearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L-0 of the film. We compute the universal ratio of the thickness of the film L-0 and the transverse correlation length xi(T) in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L-0: [L-0,L-KT/xi(T)]* = 1.595(7). This results can be compared with experimental results on thin films of He-4 near the lambda-transition.