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Self-avoiding walks and polygons on the triangular lattice

Iwan Jensen

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We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, μ = 4.150 797 226(26), and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.


Keywords

series expansions

critical exponents and amplitudes (theory)

PACS

05.40.Fb Random walks and Levy flights

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

05.10.Gg Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

MSC

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)

Subjects

Computational physics

Statistical physics and nonlinear systems

Dates

Issue 10 (October 2004)

Received 19 August 2004, accepted for publication 14 October 2004

Published 25 October 2004



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