Two-dimensional self-avoiding walks on a cylinder

We present simulations of self-avoiding random walks (SAWs) on two-dimensional 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 μ, the variance of the winding number around the cylinder, and the density of parallel contacts. While μ(L) and <W²(L,h)> scale as expected [in particular, <W²(L,h)>~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 γ of SAWs might be nonuniversal. Finally, we find that the amplitude for <W²> does not agree with naive expectations from conformal invariance.