  We study the thermodynamic Casimir force for films with various types of
boundary conditions and the bulk universality class of the three-dimensional
Ising model. To this end we perform Monte Carlo simulations of the improved
Blume-Capel model on the simple cubic lattice. In particular, we employ the
exchange or geometric cluster cluster algorithm [J.R. Heringa and H. W. J.
Bl\"ote, Phys. Rev. E 57, 4976 (1998)]. In a previous work we demonstrated that
this algorithm allows to compute the thermodynamic Casimir force for the
plate-sphere geometry efficiently. It turns out that also for the film geometry
a substantial reduction of the statistical error can achieved. Concerning
physics, we focus on (O,O) boundary conditions, where O denotes the ordinary
surface transition. These are implemented by free boundary conditions on both
sides of the film. Films with such boundary conditions undergo a phase
transition in the universality class of the two-dimensional Ising model. We
determine the inverse transition temperature for a large range of thicknesses
L_0 of the film and study the scaling of this temperature with L_0. In the
neighborhood of the transition, the thermodynamic Casimir force is affected by
finite size effects, where finite size refers to a finite transversal extension
L of the film. We demonstrate that these finite size effects can be computed by
using the universal finite size scaling function of the free energy of the
two-dimensional Ising model.
