Self-avoiding surfaces, topology, and lattice animals

With Monte Carlo simulation we study closed self-avoiding surfaces (SAS) of arbitrary genus on a cubic lattice. The gyration radius and entropic exponents are nu=0.506 +/- 0.005 and theta=1.50 +/- 0.06, respectively. Thus, SAS behave like lattice animals (LA) or branched polymers at criticality. This result, contradicting previous conjectures, is due to a mechanism of geometrical redundancy, which is tested by exact renormalization on a hierarchical vesicle model. By mapping SAS into restricted interacting site LA, we conjecture nu(THETA)=1/2 , phi(THETA)=1, and theta(THETA)=3/2 at the LA theta point.