Critical behavior of the chain-generating function of self-avoiding walks on the Sierpinski gasket family: The Euclidean limit

摘要

We study self-avoiding walks (SAW's) on the generalized Sierpinski gasket 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 series expansion for the chain-generating function of SAW's on these lattices, 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 analytic argument supporting the assumption that lim(b-->infinity) gamma(b)-->gamma(E). [References: 4]