2-d Self-Avoiding Walks on a Cylinder
Abstract
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 <W^2(L,h)> scale as as expected (in particular, <W^2(L,h)> \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 <W^2> does not agree with naive expectations from conformal invariance.
Cite
@article{arxiv.cond-mat/9808075,
title = {2-d Self-Avoiding Walks on a Cylinder},
author = {Helge Frauenkron and Maria Serena Causo and Peter Grassberger},
journal= {arXiv preprint arXiv:cond-mat/9808075},
year = {2009}
}
Comments
4 pages, 4 figures, PRL style, submitted to PRL