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

Abstract

We study the thermodynamic Casimir effect in thin films in the three-dimensionalXY universality class. To this end, we simulate the improved two-componentϕ4 model on the simple cubic lattice. We use lattices up to the thicknessL0 = 33. On thebasis of the results of our Monte Carlo simulations we compute the universal finite size scaling functionθ that characterizes the behaviour of the thermodynamic Casimir force in the neighbourhoodof the critical point. We confirm that leading corrections to the universal finite size scalingbehaviour due to free boundary conditions can be expressed using an effective thicknessL0,eff = L0+Ls, withLs = 1.02(7). Our results are compared with experiments on films of 4He nearthe λ-transition, previous Monte Carlo simulations of theXY modelon the simple cubic lattice and field-theoretic results. Our result for the finite size scaling functionθ is essentially consistent with the experiments on films of 4He and the previous Monte Carlo simulations.