CRITICAL-BEHAVIOR OF THE CHAIN-GENERATING FUNCTION OF SELF-AVOIDING WALKS ON THE SIERPINSKI GASKET FAMILY - THE EUCLIDEAN LIMIT

We study self-avoiding walks (SAW's) on the generalized Sierpinski gas ket family of fractals. Each fractal can be labeled by an integer b (2 less than or equal to b less than or equal to infinity), so that the fractal and spectral dimensions tend to the Euclidean value 2 when b-- >infinity. By using an exact enumeration technique to obtain the serie s expansion for the chain-generating function of SAW's on these lattic es, we calculate the associated critical exponent gamma(b) for 2 less than or equal to b less than or equal to 100. The large-b behavior of gamma(b) is the first numerical result consistent with the asymptotic convergence toward the Euclidean value gamma(E). We also give an analy tic argument supporting the assumption that lim(b-->infinity) gamma(b) -->gamma(E).