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

TL;DR

This study uses Monte Carlo simulations to analyze the Kosterlitz-Thouless transition in thin films within the 3D XY universality class, confirming theoretical predictions and providing universal ratios relevant for experiments.

Contribution

It presents a high-precision finite size scaling analysis of the KT transition in thin films using improved lattice models, confirming RG theory predictions.

Findings

Confirmed KT nature of the transition through multiple finite size scaling indicators.

Computed a universal ratio [L_{0,KT}/\xi_T]^* = 1.595(7) for thin films.

Validated the scaling of transition temperature with film thickness against RG theory.

Abstract

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 \Upsilon 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. The predictions of the renormalization group (RG) theory are confirmed. We compute the universal ratio of the thickness of the film L_0 and the transversal 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,KT}/\xi_T]^* = 1.595(7). This results can be compared with experimental results on thin films of 4He near the \lambda-transition.