Quenched averages for self-avoiding walks and polygons on deterministic fractals

Sumedha, . ; Dhar, Deepak (2006) Quenched averages for self-avoiding walks and polygons on deterministic fractals Journal of Statistical Physics, 125 (1). pp. 55-76. ISSN 0022-4715

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Official URL: https://link.springer.com/article/10.1007/s10955-0...

Related URL: http://dx.doi.org/10.1007/s10955-006-9098-7


We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks Wn(S), and rooted self-avoiding polygons Pn(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for Pn(S), and Wn(S) for an arbitrary point S on the lattice. These are used to compute the averages ⟨Pn(S)⟩,⟨Wn(S)⟩,⟨logPn(S)⟩ and ⟨logWn(S)⟩ over different positions of S. We find that the connectivity constant μ, and the radius of gyration exponent ν are the same for the annealed and quenched averages. However, ⟨logPn(S)⟩≃nlogμ+(αq−2)logn, and ⟨logWn(S)⟩≃nlogμ+(γq−1)logn, where the exponents αq and γq, take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives αq≃0.72837±0.00001; and γq≃1.37501±0.00003, to be compared with the known annealed values αa=0.73421 and γq=1.37522.

Item Type:Article
Source:Copyright of this article belongs to Springer Verlag.
Keywords:Self-Avoiding Walks; Random Media; Fractals
ID Code:112286
Deposited On:31 Jan 2018 04:29
Last Modified:31 Jan 2018 04:29

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