Mean Area of Self-Avoiding Loops

Abstract

The mean area of two-dimensional unpressurised vesicles, or self-avoiding loops of fixed length $N$, behaves for large $N$ as $A_0{N}^{3/2}$, while their mean square radius of gyration behaves as $R_0^2{N}^{3/2}$. The amplitude ratio $A_0/R_0^2$ is computed exactly and found to equal $4\pi /5$. The physics of the pressurised case, both in the inflated and collapsed phases, may be usefully related to that of a complex O(n) field theory coupled to a U(1) gauge field, in the limit $n\to 0$.

12 pages, plain TeX, (one TeX macro omission corrected)