Iwan Jensen 2004 J. Phys. A: Math. Gen. 37 11521 doi:10.1088/0305-4470/37/48/001
Iwan Jensen
Show affiliationsWe calculate improved lower bounds for the connective constants for self-avoiding walks on the square, hexagonal, triangular, (4.82) and (3.122) lattices. The bound is found by Kesten's method of irreducible bridges. This involves using transfer-matrix techniques to exactly enumerate the number of bridges of a given span to very many steps. Upper bounds are obtained from recent exact enumeration data for the number of self-avoiding walks and compared to current best available upper bounds from other methods.
05.50.+q Lattice theory and statistics (Ising, Potts, 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 48 (3 December 2004)
Received 10 September 2004, in final form 8 October 2004
Published 17 November 2004
Iwan Jensen 2004 J. Phys. A: Math. Gen. 37 11521
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