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 φ4 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 ∝L0-1 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