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

Abstract

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 $γ\gtapprox 1.3425(3)$, 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.

24 pages, LaTeX2e, 4 figures

References in corpus (3)

• 2-d Self-Avoiding Walks on a Cylinder
• On the Non-Universality of a Critical Exponent for Self-Avoiding Walks
• Winding angles for two-dimensional polymers with orientation dependent interactions

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