  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.
