Scaling Behavior of Self-Avoiding Random Surfaces

Self-avoiding random surfaces are analyzed by renormalization-group methods. The Hausdorff dimension $\frac{1}{\nu }$ and the critical plaquette fugacity are computed for different dimensionalities $d$; in particular, $\nu =\frac{1}{2}-\frac{\epsilon }{4}+O\left({\epsilon }^2\right)$ for $d=2+\epsilon$. The model describes "sheet polymers" in a good solvent: A Flory type of argument yields $\nu =\frac{3}{\mathrm{}(4+d)\mathrm{}}$, in good agreement with the renormalization results, and a critical dimensionality $d_c=8\mathrm{}$, with $\nu =\frac{1}{4}$.