Scaling Behavior of Self-Avoiding Random Surfaces

Abstract

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