Iwan Jensen 2004 J. Phys. A: Math. Gen. 37 11521 doi:10.1088/0305-4470/37/48/001
Improved lower bounds on the connective constants for two-dimensional self-avoiding walks
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.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 48 (3 December 2004)
Received 10 September 2004, in final form 8 October 2004
Published 17 November 2004
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Improved lower bounds on the connective constants for two-dimensional self-avoiding walks
Iwan Jensen 2004 J. Phys. A: Math. Gen. 37 11521
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