Coherent-anomaly method in self-avoiding walk problems

Xiao Hu and Masuo Suzuki

Physica A: Statistical Mechanics and its Applications, 1988, vol. 150, issue 2, 310-323

Abstract: Self-avoiding walk (SAW), being a nonequilibrium cooperative phenomenon, is investigated with a finite-order-restricted-walk (finite-ORW or FORW) coherent-anomaly method (CAM). The coefficient β1r in the asymptotic form Cnr≅ β1r λn1r for the total number Cnr of r- ORW's with respect to the step number n is investigated for the first time. An asymptotic form for SAW's is thus obtained form the series of FORW approximants, Cnr≅ brgμn(1 + a/r)n, as the envelope curve Cn≅b(ae/g)gμnng. Numerical results are given by Cn≅1.424n0.27884.1507n and Cn≅1.179n0.158710.005n for the plane triangular lattice and f.c.c. lattice, respectively. A good coincidence of the total numbers estimated from the above simple formulae with exact enumerations for finite-step SAW's implies that the essential nature of SAW (non-Markov process) can be understood from FORW (Markov process) in the CAM framework.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:150:y:1988:i:2:p:310-323

DOI: 10.1016/0378-4371(88)90154-9

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