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 φ4 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 L0 = 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 U4, the second moment correlation length over the lattice size ξ2nd/L, the ratio of the partition functions with antiperiodic and periodic boundary conditions Za/Zp and the helicity modulus Υ clearly confirm the Kosterlitz-Thouless nature of the transition. We analyse the scaling of the transition temperature with the thickness L0 of the film. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L0 and the transversal correlation length ξT in the three-dimensional thermodynamic limit at the Kosterlitz-Thouless transition temperature of a film of thickness L0: [L0,KT/ξT ] ∗ = 1.595(7). This results can be compared with experimental results on thin films of 4He near the λ-transition.