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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Official URL: http://jmp.aip.org/resource/1/jmapaq/v19/i1/p5_s1?...

Related URL: http://dx.doi.org/10.1063/1.523515

## Abstract

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^{n}n^{γ-1}, μ^{n}n^{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.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Institute of Physics. |

ID Code: | 9291 |

Deposited On: | 02 Nov 2010 12:33 |

Last Modified: | 02 Nov 2010 12:33 |

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