Discrete solid-on-solid model of interface with bending rigidity: Roughening versus crumpling

We propose a discrete solid-on-solid model of interface having a specific type of bending rigidity; this type of bending rigidity was introduced originally by Widom [J. Chem. Phys. 84, 6943 (1986)] to account for the energy cost associated with the bending of the oil-water interface in a lattice model of ternary microemulsions. We calculate the width of the interface as well as various height-height and normal-normal correlation functions through Monte Carlo simulation. We show that when this specific ‘‘bending energy’’ alone controls the out-of-plane thermal fluctuations of our discrete interface, the membrane is crumpled at all nonvanishing temperatures, but the nature of this crumpling is very different from that observed in the standard continuum models. We also show the effects of a pinning potential and present results on some nonequilibrium properties of the model. © 1996 The American Physical Society.