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Self-avoiding random walks: Some exactly soluble cases

Dhar, Deepak (1978) Self-avoiding random walks: Some exactly soluble cases. Journal of Mathematical Physics, 19 (1). pp. 5-11. ISSN 0022-2488. doi:10.1063/1.523515.

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We use the exact renormalization group equations to determine the asymptotic behavior of long self‐avoiding random walks on some pseudolattices. The lattices considered are the truncated 3‐simplex, the truncated 4‐simplex, and the modified rectangular lattices. The total number of random walks C_n, the number of polygons P_n of perimeter n, and the mean square end to end distance 〈R^2_n〉 are assumed to be asymptotically proportional to μ^nn^(γ−1), μ^nn^(α−3), and n^(2ν) respectively for large n, where n is the total length of the walk. The exact values of the connectivity constant μ, and the critical exponents λ, α, ν are determined for the three lattices. We give an example of two lattice systems that have the same effective nonintegral dimensionality 3/2 but different values of the critical exponents γ, α, and ν.

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Additional Information:© 1978 American Institute of Physics. Received 12 July 1977. Online Publication Date: 11 August 2008. It is a pleasure to thank Professor Jon Mathews for many discusssions and critical comments, and Ms. RLou Norquist for typing the manuscript.
Issue or Number:1
Classification Code:PACS: 64.60.Cn, 05.70.Fh
Record Number:CaltechAUTHORS:20120730-072812701
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Official Citation: Self‐avoiding random walks: Some exactly soluble cases Deepak Dhar J. Math. Phys. 19, 5 (1978);
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32778
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2012 16:46
Last Modified:09 Nov 2021 21:29

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