POLYMERS ON FRACTAL LATTICES

We study the critical exponents of self avoiding walks on a family of Sierpinski-type fractals. The members of the family are characterized by an integer b. For large values of b, both the Hausdorff and the spectral dimensions of the fractals tend to 2 from below. We use finite size scaling theory to determine the first two terms in the asymptotic expansions of size exponent ν and the susceptibility exponent γ for large b. The results are compared to predictions of phenomenological theories such as Flory's, and to the ε-expansion techniques.