D MacDonald et al 2000 J. Phys. A: Math. Gen. 33 5973 doi:10.1088/0305-4470/33/34/303
D MacDonald1, S Joseph2, D L Hunter1, L L Moseley2, N Jan1 and A J Guttmann3
Show affiliationsWe have substantially extended the series for the number of self-avoiding walks and the mean-square end-to-end distance on the simple cubic lattice. Our analysis of the series gives refined estimates for the critical point and critical exponents. Our estimates of the exponents γ and ν are in good agreement with recent high-precision Monte Carlo estimates, and also with recent renormalization group estimates. Critical amplitude estimates are also given. A new, improved rigorous upper bound for the connective constant µ<4.7114 is obtained.
05.40.Fb Random walks and Levy flights
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Issue 34 (1 September 2000)
Received 17 March 2000
D MacDonald et al 2000 J. Phys. A: Math. Gen. 33 5973
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