Iwan Jensen J. Stat. Mech. (2004) P10008 doi:10.1088/1742-5468/2004/10/P10008
Iwan Jensen
Show affiliationsWe 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.
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.)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 10 (October 2004)
Received 19 August 2004, accepted for publication 14 October 2004
Published 25 October 2004
Iwan Jensen J. Stat. Mech. (2004) P10008
R-D Herzberg et al 2006 Phys. Scr. 2006 73
Joachim Krug J. Stat. Mech. (2007) P07001
J C Woicik et al 2005 Phys. Scr. 2005 620
Miloslav Znojil 2008 J. Phys. A: Math. Theor. 41 215304
Mariano A Zimmler et al 2007 Nanotechnology 18 235205
Bojko Bakalov et al 2008 J. Phys. A: Math. Theor. 41 194002
Kimball A Milton and Jef Wagner 2008 J. Phys. A: Math. Theor. 41 155402
S L Rumyantsev et al 2008 Semicond. Sci. Technol. 23 105001
Sergei K Suslov 2009 J. Phys. B: At. Mol. Opt. Phys. 42 185003