Scaling Behavior of Self-Avoiding Random Surfaces

Self-avoiding random surfaces are analyzed by renormalization-group methods. The Hausdorff dimension 1/\u3bd and the critical plaquette fugacity are computed for different dimensionalities d; in particular, \u3bd=1/2-\u3b5/4+O(\u3b52) for d=2+\u3b5. The model describes "sheet polymers" in a good solvent: A Flory type of argument yields \u3bd=3/(4+d), in good agreement with the renormalization results, and a critical dimensionality dc=8, with \u3bd=1/4