On the non-universality of a critical exponent for self-avoiding walks |
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| Institution: | 1. Department of Biology, Johns Hopkins University, 3400 N Charles St., Baltimore, MD 21218, USA;2. Department of Biophysics, Johns Hopkins University, 3400 N Charles St., Baltimore, MD 21218, USA;3. CMDB Graduate Program, Johns Hopkins University, 3400 N Charles St., Baltimore, MD 21218, USA |
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| Abstract: | 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 γ = 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 γ. The lattice topology of the Manhattan lattice precludes such parallel steps. |
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