A strong-coupling analysis of two-dimensional O(N) sigma models with $N\ge 3$ on square, triangular and honeycomb lattices

Abstract

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free $\mathrm{O}(N)$ 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. All 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 per mille even down to $N=3$.

Comments: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfig