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 $N=3$.

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

References in corpus (4)

• New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices
• Four-point renormalized coupling constant in O(N) models
• Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at correlation length $4\times 10^5$
• Advanced Linked Cluster Expansion. Scalar Fields at Finite Temperature

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• Perturbative renormalization group, exact results and high temperature series to order 21 for the N-vector spin models on the square lattice
• Comparison of the O(3) Bootstrap $\sigma$-Model with the Lattice Regularization at Low Energies
• The Intrinsic Coupling in Integrable Quantum Field Theories
• Continuum Limits and Exact Finite-Size-Scaling Functions for One-Dimensional $O(N)$-Invariant Spin Models
• On the evaluation of universal non-perturbative constants in O(N) sigma models
• On Statistical Mechanics of Instantons in the CP^{N_c-1} Model
• Quasi-asymptotic freedom in the two dimensional O(3) model
• The Gross-Neveu model and QCDs chiral phase transition