Self-avoiding walks and polygons on the triangular lattice

Abstract

We use new algorithms, based on the finite lattice method of series expansion, to extendthe enumeration of self-avoiding walks and polygons on the triangular lattice to length 40and 60, respectively. For self-avoiding walks to length 40 we also calculate series for themetric properties of mean-square end-to-end distance, mean-square radius ofgyration and the mean-square distance of a monomer from the end points. Forself-avoiding polygons to length 58 we calculate series for the mean-square radiusof gyration and the first 10 moments of the area. Analysis of the series yieldsaccurate estimates for the connective constant of triangular self-avoiding walks,μ = 4.150 797 226(26), and confirms to a high degree of accuracy several theoretical predictions for universalcritical exponents and amplitude combinations.