Universal amplitude combinations for self-avoiding walks and polygons on the honeycomb lattice

Abstract

We have calculated exactly the mean-square end-to-end distance, the mean-square radius of gyration, and the mean-square distance of a monomer from the origin, for n-step self-avoiding walks on the honeycomb lattice up to 46 steps. We also calculated the mean-square radius of gyration and moments of area for n-step self-avoiding polygons on the honeycomb lattice up to 60 steps. We estimated the critical amplitudes and our numerical results are consistent with the theoretical predictions by the universality for certain amplitude combinations.