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Exact enumeration of parallel walks on directed lattices

J W Essam

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Mutually avoiding pairs of parallel walks on a number of d-dimensional lattices are mapped onto undirected random walks which return to the origin on a projected (d-1)-dimensional lattice. Generating functions for the number of such pairs of a given length are thus expressed in terms of standard Green's functions. Directed lattices considered include the directed hypercubic and body-centred hypercubic. The generating function for a directed triangular lattice is also obtained. This work is a generalization of known results for the square lattice.


PACS

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

05.40.Fb Random walks and Levy flights

MSC

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

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

Subjects

Statistical physics and nonlinear systems

Dates

Issue 17 (7 September 1993)



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