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Recently-generated long strong-coupling series for the two-point Green'sfunctions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ models areanalyzed, focusing on the evaluation of dimensionless renormalization-groupinvariant ratios of physical quantities and applying resummation techniques toseries in the inverse temperature $\beta$ and in the energy $E$. Square,triangular, and honeycomb lattices are considered, as a test of universalityand in order to estimate systematic errors. Large-$N$ solutions are carefullystudied in order to establish benchmarks for series coefficients andresummations. Scaling and universality are verified. All invariant ratiosrelated to the large-distance properties of the two-point functions varymonotonically with $N$, departing from their large-$N$ values only by a few permille even down to $N=3$.Comment: 53 pages (incl. 5 figures), tar/gzip/uuencode, REVTEX + psfi

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Strong-coupling analysis of two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">O</mml:mi><mml:mn /><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo><mml:mn /></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>σ</mml:mi></mml:math>models with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>&gt;~</mml:mo><mml:mn>3</mml:mn></mml:math>…

Strong-coupling analysis of two-dimensionalO(N)σmodels withN>~3…