The specific heat of thin films near the λ-transition: a Monte Carlo study of an improved three-dimensional lattice model

We study the finite size scaling behaviour of the specific heat of thin films in the neighbourhood of the λ-transition. To this end we have simulated the improved two-component phi⁴ model on the simple cubic lattice. We employ free boundary conditions in the short direction to mimic the vanishing order parameter at the boundaries of a ⁴He film. Most of our simulations are performed for the thicknesses L₀ = 8, 16 and 32 of the film. It turns out that one has to take into account corrections {\propto }

L_0^{-1} to obtain a good collapse of the finite size scaling functions obtained from different L₀. Our results are compared with those obtained from experiments on thin films of ⁴He near the λ-transition, from field theory and from previous Monte Carlo simulations.