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 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 expected [in particular, [W(2)(L,h)]similar to 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 SAWs might be nonuniversal. Finally, we find that the amplitude for [W(2)] does not agree with naive expectations from conformal invariance. [S1063-651X(99)51201-4].