Two-dimensional 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 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.Comment: 4 pages, 4 figures, PRL style, submitted to PR