2-d Self-Avoiding Walks on a Cylinder

TL;DR

This paper investigates self-avoiding walks on a cylindrical 2D lattice, analyzing their size, connectivity, winding, and contact density, revealing unexpected decay patterns and challenging previous theories about universality and conformal invariance.

Contribution

The study provides new simulation data on self-avoiding walks on a cylindrical lattice, challenging existing predictions about contact decay and universality of critical exponents.

Findings

Connectivity constant scales with L as expected

Winding number variance scales as h/L

Number of parallel contacts decays as h/L^1.92

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.