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

Massimo Campostrini·Andrea Pelissetto·Paolo Rossi·Ettore Vicari
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Abstract

Recently-generated long strong-coupling series for the two-point Green's functions of asymptotically free ${\rm O}(N)$ lattice $σ$ 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 $β$ 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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Massimo Campostrini, Andrea Pelissetto, Paolo Rossi, Ettore Vicari. 1996-02-08. A strong-coupling analysis of two-dimensional O(N) sigma models with $N\geq 3$ on square, triangular and honeycomb lattices. https://doi.org/10.1103/physrevd.54.1782

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