Scaling behavior of fluid membranes in three dimensions

The scaling behavior of self-avoiding (SA) fluid membranes in three dimensions subject to a bending rigidity {κ} is studied by Monte Carlo simulation. For {κ}=0, open and closed membranes behave like SA branched polymers at large length scales. For arbitrary {κ}, scaling functions of the combination y==N1/2/{κ} are found to describe the shape variables of closed membranes. The transition from a rigid phase at small y to a SA branched polymer phase at large y is smooth for closed membranes.