New Renormalization Group Results for Scaling of Self-Avoiding Tethered Membranes

TL;DR

This paper applies renormalization group techniques to analyze the scaling behavior of self-avoiding polymerized membranes, providing second-order calculations of the scaling exponent and comparing results with existing estimates.

Contribution

It introduces second-order renormalization group calculations for self-avoiding membranes and compares the results with known theoretical estimates.

Findings

Scaling exponent nu calculated to order epsilon^2

Results agree with Gaussian variational estimate at large d

Close to Flory estimate for d=3

Abstract

The scaling properties of self-avoiding polymerized 2-dimensional membranes are studied via renormalization group methods based on a multilocal operator product expansion. The renormalization group functions are calculated to second order. This yields the scaling exponent nu to order epsilon^2. Our extrapolations for nu agree with the Gaussian variational estimate for large space dimension d and are close to the Flory estimate for d=3. The interplay between self-avoidance and rigidity at small d is briefly discussed.