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

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

1996-02-08

arxiv.org/abs/hep-lat/9602011v1

Phys.Rev. D54 (1996) 1782-1808

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

10.1103/PhysRevD.54.1782

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ 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 $N=3$.

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