Scaling of confined membranes and interfaces

Abstract

We have carried out Monte Carlo studies of the probability distribution functions (PDFS) for models of two- and three-dimensional membranes and interfaces confined between two parallel repulsive walls separated by a distance D. For two-dimensional interfaces it is known that the position PDF p(z), for conformally mapped binding potentials, scales and is characterized by a universal scaling function p(z) approximately sin pi z/Dtheta -1 (where theta is the short distance expansion critical exponent) for strong, weak and intermediate fluctuation regimes. Our simulation studies show that for a variety of membrane models the PDF has the expected scaling p(z)=U(z/D)/D, and we find that the same parametrization of the membrane PDFs gives an excellent fit to the numerical data.