Critical exponent gamma for self-avoiding walks on the Sierpinski gasket family of fractals

Abstract

The authors apply the Monte Carlo renormalization group (MCRG) analysis of self-avoiding walks (SAWs) on fractals to calculate the critical exponent gamma , associated with the total number of distinct SAWs. In the case of the Sierpinski gasket family of fractals (whose members are labelled by an integer b, 2<or=b< infinity ) they have calculated gamma for 2<or=b<or=80. Their MCRG results deviate at most 0.2% from the available exact results (2<or=b<or=8). The entire set of their results demonstrates that gamma , being always larger than the Euclidean value 43/32, monotonically increases with b.