On the Non-Universality of a Critical Exponent for Self-Avoiding Walks

Details On the Non-Universality of a Critical Exponent for Self-Avoiding Walks On the Non-Universality of a Critical Exponent for Self-Avoiding Walks

1998-05-12

arxiv.org/abs/cond-mat/9805146v1

Physics

Condensed Matter

Statistical Mechanics

34 pages, 3 figures

Scientific paper

10.1016/S0550-3213(98)00419-2

We have extended the enumeration of self-avoiding walks on the Manhattan lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps. Analysis of this data suggests that the walk generating function exponent gamma = 1.3385 +- 0.003, which is different from the corresponding exponent on the square, triangular and honeycomb lattices. This provides numerical support for an argument recently advanced by Cardy, to the effect that excluding walks with parallel nearest-neighbour steps should cause a change in the exponent gamma. The lattice topology of the Manhattan lattice precludes such parallel steps.

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