  The fluctuation pressure of a lipid-bilayer membrane is important for the
stability of lamellar phases and the adhesion of membranes to surfaces. In
contrast to many theoretical studies, which predict a decrease of the pressure
with the cubed inverse distance between the membranes, Freund suggested very
recently a linear inverse distance dependence [Proc. Natl. Acad. Sci. U.S.A.
110, 2047 (2013)]. We address this discrepancy by performing Monte Carlo
simulations for a membrane model discretized on a square lattice and employ the
wall theorem to evaluate the pressure for a single membrane between parallel
walls. For distances that are small compared with the lattice constant, the
pressure indeed depends on the inverse distance as predicted by Freund. For
intermediate distances, the pressure depends on the cubed inverse distance as
predicted by Helfrich [Z. Naturforsch. A 33, 305 (1978)]. Here, the crossover
length between the two regimes is a molecular length scale. Finally, for
distances large compared with the mean squared fluctuations of the membrane,
the entire membrane acts as a soft particle and the pressure on the walls again
depends linearly on the inverse distance.
