Branched Polymers on the Given-Mandelbrot family of fractals

Deepak Dhar

Paper

Branched Polymers on the Given-Mandelbrot family of fractals

Abstract

We study the average number A_n per site of the number of different configurations of a branched polymer of n bonds on the Given-Mandelbrot family of fractals using exact real-space renormalization. Different members of the family are characterized by an integer parameter b, b > 1. The fractal dimension varies from

to 2 as b is varied from 2 to infinity. We find that for all b > 2, A_n varies as

, where

and

are some constants, and

. We determine the exponent

, and the size exponent

(average diameter of polymer varies as

), exactly for all b > 2. This generalizes the earlier results of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988].