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

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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 Cn, the number of polygons Pn of perimeter n, and the mean square end to end distance <R2n> are assumed to be asymptotically proportional to μnnγ-1, μnnα-3, and n 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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ID Code:9291
Deposited On:02 Nov 2010 12:33
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