CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20120730-072812701

[img]
Preview
PDF - Published Version
See Usage Policy.

493Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20120730-072812701

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^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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org//10.1063/1.523515 DOIUNSPECIFIED
http://jmp.aip.org/resource/1/jmapaq/v19/i1/p5_s1PublisherUNSPECIFIED
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
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20120730-072812701
Official Citation: Self‐avoiding random walks: Some exactly soluble cases Deepak Dhar J. Math. Phys. 19, 5 (1978); http://dx.doi.org/10.1063/1.523515
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32778
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2012 16:46
Last Modified:03 Oct 2019 04:03

Repository Staff Only: item control page