Journal article

Self-avoiding walks on the simple cubic lattice

D MacDonald, S Joseph, DL Hunter, LL Moseley, N Jan, AJ Guttmann

Journal of Physics A: Mathematical and Theoretical | Published : 2000


We 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 v 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.

University of Melbourne Researchers

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