  Quantitative theory of interbilayer interactions is essential to interpret
x-ray scattering data and to elucidate these interactions for biologically
relevant systems. For this purpose Monte Carlo simulations have been performed
to obtain pressure P and positional fluctuations sigma. A new method, called
Fourier Monte-Carlo (FMC), that is based on a Fourier representation of the
displacement field, is developed and its superiority over the standard method
is demonstrated. The FMC method is applied to simulating a single membrane
between two hard walls, which models a stack of lipid bilayer membranes with
non-harmonic interactions. Finite size scaling is demonstrated and used to
obtain accurate values for P and sigma in the limit of a large continuous
membrane. The results are compared with perturbation theory approximations, and
numerical differences are found in the non-harmonic case. Therefore, the FMC
method, rather than the approximations, should be used for establishing the
connection between model potentials and observable quantities, as well as for
pure modeling purposes.
