2-d Self-Avoiding Walks on a Cylinder

Details 2-d Self-Avoiding Walks on a Cylinder 2-d Self-Avoiding Walks on a Cylinder

1998-08-07

arxiv.org/abs/cond-mat/9808075v1

Phys. Rev. E Vol. 59 (1999) R16-R19

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures, PRL style, submitted to PRL

Scientific paper

10.1103/PhysRevE.59.R16

We present simulations of self-avoiding random walks on 2-d lattices with the topology of an infinitely long cylinder, in the limit where the cylinder circumference L is much smaller than the Flory radius. We study in particular the L-dependence of the size h parallel to the cylinder axis, the connectivity constant mu, the variance of the winding number around the cylinder, and the density of parallel contacts. While mu(L) and scale as as expected (in particular, \sim h/L), the number of parallel contacts decays as h/L^1.92, in striking contrast to recent predictions. These findings strongly speak against recent speculations that the critical exponent gamma of SAW's might be nonuniversal. Finally, we find that the amplitude for does not agree with naive expectations from conformal invariance.

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