The thermodynamic Casimir effect in the neighbourhood of the lambda-transition: A Monte Carlo study of an improved three dimensional lattice model

TL;DR

This study uses Monte Carlo simulations of an improved three-dimensional XY model to analyze the universal finite size scaling function of the thermodynamic Casimir effect near the lambda-transition, confirming consistency with experimental data.

Contribution

It provides a detailed Monte Carlo analysis of the thermodynamic Casimir effect in the 3D XY universality class, including corrections to scaling and comparison with experiments.

Findings

Universal finite size scaling function theta computed.

Leading corrections to scaling expressed via effective thickness L_{0,eff}.

Results agree with experiments on 4He films and previous simulations.

Abstract

We study the thermodynamic Casimir effect in thin films in the three dimensional XY universality class. To this end, we simulate the improved two component phi^4 model on the simple cubic lattice. We use lattices up to the thickness L_0=33. Based on the results of our Monte Carlo simulations we compute the universal finite size scaling function theta that characterizes the behaviour of the thermodynamic Casimir force in the neighbourhood of the critical point. We confirm that leading corrections to the universal finite size scaling behaviour due to free boundary conditions can be expressed by an effective thickness L_{0,eff} = L_0+ L_s, with L_s =1.02(7). Our results are compared with experiments on films of 4He near the lambda-transition, previous Monte Carlo simulations of the XY model on the simple cubic lattice and field-theoretic results. Our result for the finite size scaling function theta is essentially consistent with the experiments on films of 4He and the previous Monte Carlo simulations.