Strong-coupling analysis of two-dimensional O(N) a models with N>=3 on square, triangular, and honeycomb lattices

Recently generated long strong-coupling series for the two-point Green's functions of asymptotically free O(N) lattice sigma models are analyzed, focusing on the evaluation of dimensionless renormalization-group-invariant ratios of physical quantities and applying resummation techniques to series in the inverse temperature beta and in the energy E. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-N solutions are carefully studied in order to establish benchmarks for series coefficients and resummations. Scaling and universality are verified. Ali invariant ratios related to the large-distance properties of the two-point functions vary monotonically with N, departing from their large-N values only by a few pet mille even down to N=3.