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 $lo{g}_{{}_2}3$ to 2 as b is varied from 2 to infinity. We find that for all b > 2, A_n varies as ${\lambda }^{n}exp(b{n}^{\psi })$, where $\lambda$ and $b$ are some constants, and $0<\psi <1$. We determine the exponent $\psi$, and the size exponent $\nu$ (average diameter of polymer varies as $n^{\nu }$), exactly for all b > 2. This generalizes the earlier results of Knezevic and Vannimenus for b = 3 [Phys. Rev {\bf B 35} (1987) 4988].

24 pages, 8 figures

Cited by in corpus (8)

• Spanning trees on the Sierpinski gasket
• Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices
• Dimer-monomer model on the Sierpinski gasket
• Scaling of Hamiltonian walks on fractal lattices
• Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
• Acyclic orientations on the Sierpinski gasket
• Ice model and eight-vertex model on the two-dimensional Sierpinski gasket
• Structure of spanning trees on the two-dimensional Sierpinski gasket