Self-avoiding walks in wedges
- 1 January 1985
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 18 (1) , 101-111
- https://doi.org/10.1088/0305-4470/18/1/022
Abstract
The authors consider the number of self-avoiding walks confined to a subset Zd(f) of the d-dimensional hypercubic lattice Zd, such that the coordinates (x1,x2, . . .,xd) of each vertex in the walk satisfy x1>or=0 and 0kk(x1) for k=2,3, . . .,d. They show that if fk(x) to infinity as x to infinity , the connective constant of walks in Zd(f) is identical to the convective constant of walks in Zd. They also explore conditions on fk which lead to a smaller connective constant for walks in Zd(f) and, in particular, consider walks between two parallel (d-1)-dimensional hyperplanes. Finally they contrast some of these results with recent work by Grimmett on percolation on subsets of the square lattice.Keywords
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