Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice

Details Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice

1998-12-16

arxiv.org/abs/cond-mat/9812267v1

J.Phys.A32:2931-2948,1999

Physics

Condensed Matter

Statistical Mechanics

24 pages, LaTeX2e, 4 figures

Scientific paper

10.1088/0305-4470/32/16/004

We present a high-statistics Monte Carlo determination of the exponent gamma for self-avoiding walks on a Manhattan lattice in two dimensions. A conservative estimate is $\gamma \gtapprox 1.3425(3)$, in agreement with the universal value 43/32 on regular lattices, but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations. We find strong corrections to scaling that seem to indicate the presence of a non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma = 1.3436(3), where the error is purely statistical.

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