FROM BUNCHES OF MEMBRANES TO BUNDLES OF STRINGS

Bunches of membranes and bundles of strings exhibit unbinding transitions from a bound state at low temperatures to an unbound state at high temperatures. N freely suspended manifolds unbind continuously at the unique unbinding temperature T-u(f) which is independent of N. The amplitudes of the critical singularities have a strong N-dependence, however, which implies that the critical region for the continuous transition becomes very small and the transition becomes very abrupt in the limit of large N. If N membranes or strings are bound to a rigid surface, they undergo a sequence of either two or of N successive transitions. In general, the rigid surface affects the contact probabilities of the fluctuating manifolds. For effectively repulsive interactions, the contact exponent zeta(2) which governs the probability for local pair contacts satisfies the scaling relation zeta(2) = d(parallel to) + zeta where d(parallel to) and zeta denote the dimensionality and the roughness exponent of these manifolds.