Branched polymers on the given-mandelbrot family of fractals

Dhar, Deepak (2005) Branched polymers on the given-mandelbrot family of fractals Physical Review E, 71 (3). 031801_1-031801_8. ISSN 1063-651X

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We study the average number An 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, 2≤b≤∞. The fractal dimension varies from log2 3 to 2 as b is varied from 2 to ∞. We find that for all b≥3, An varies as λn exp(bnψ), where λ and b are some constants, and 0<ψ<1. We determine the exponent ψ, and the size exponent ν (average diameter of polymer varies as nν), exactly for all b, 3≤b≤∞. This generalizes the earlier results of Knezevic and Vannimenus for b=3 [Phys. Rev B 35, 4988 (1987)].

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:9299
Deposited On:02 Nov 2010 12:32
Last Modified:16 May 2016 19:07

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