Local contacts of membranes and strings

Local contacts within bundles of strings and buchnes of membranes are studied using transfer matrix methods, scaling theories, and Monte Carlo simulations. The contact probabilities exhibit scaling laws and decay as inverse power laws 1/ℓζn/ζ with increasing separation ℓ of the manifolds, where ζ denotes the corresponding roughness exponent. The contact exponents ζn have different values away from the boundaries of the system and close to those boundaries. These results imply that local contacts are less frequent than suggested by the widely used picture in which the fluctuation-induced interaction is interpreted in terms of collisions. In fact, deep within the bundle or bunch, one has, on average, only one pair collision per ℓ humps.