Fluctuation pressure of a stack of membranes

We calculate the universal constants in Helfrich's pressure law for a stack of N membranes between walls by strong-coupling theory. Using the close analogy between this system and a stack of strings, where the universal constants are exactly known, we construct a smooth potential that keeps the membranes apart. The strong-coupling limit of the perturbative treatment of the free energy yields pressure constants for an arbitrary number of membranes, which are in very good agreement with values from Monte Carlo simulations.