Critical exponents of self-avoiding walks on fractals with dimension 2-ε

Abstract

We study critical exponents of self-avoiding walks on a family of finitely ramified Sierpinki-type fractals. The members of the family are characterized by an integer b, 2 ≤ b < ∞. For large b, the fractal dimension of the lattice tends to 2 from below. We use scaling theory to determine the critical exponents for large b. We show that as b → ∞ the susceptibility exponent does not tend to its 2-dimensional value, and determine the leading correction to critical exponents for large but finite b.