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Mean Area of Self-Avoiding Loops

John Cardy
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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 $R^2_0 N^{3/2}$. The amplitude ratio $A_0/R_0^2$ is computed exactly and found to equal $4π/5$. 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 $n \to 0$.

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John Cardy. 1993-10-11. Mean Area of Self-Avoiding Loops. https://doi.org/10.1103/physrevlett.72.1580

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