  We study the thermodynamic Casimir force for films in the three-dimensional
Ising universality class with symmetry breaking boundary conditions. To this
end we simulate the improved Blume-Capel model on the simple cubic lattice. We
study the two cases ++, where all spins at the boundary are fixed to +1 and +-,
where the spins at one boundary are fixed to +1 while those at the other
boundary are fixed to -1. An important issue in analyzing Monte Carlo and
experimental data are corrections to scaling. Since we simulate an improved
model, leading corrections to scaling, which are proportional to L_0^-omega,
where L_0 is the thickness of the film and omega approx 0.8, can be ignored.
This allows us to focus on corrections to scaling that are caused by the
boundary conditions. We confirm the theoretical expectation that these
corrections can be accounted for by an effective thickness L_0,eff = L_0 + L_s.
Studying the correlation length of the films, the energy per area, the
magnetization profile and the thermodynamic Casimir force at the bulk critical
point we find L_s=1.9(1) for our model and the boundary conditions discussed
here. Using this result for L_s we find a nice collapse of the finite size
scaling curves obtained for the thicknesses L_0=8.5, 16.5 and 32.5 for the full
range of temperatures that we consider. We compare our results for the finite
size scaling functions theta_++ and theta_+- of the thermodynamic Casimir force
with those obtained in a previous Monte Carlo study, by the de Gennes-Fisher
local-functional method, field theoretic methods and an experiment with a
binary mixture.
