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

## TL;DR

This paper analyzes strong-coupling series for two-dimensional O(N) sigma models on various lattices, verifying universality and scaling, and providing benchmarks through large-N solutions, with results showing minimal deviation from large-N values even at N=3.

## Contribution

It introduces a comprehensive analysis of strong-coupling series for O(N) sigma models on different lattices, including large-N benchmarks and universality verification.

## Key findings

- Invariant ratios vary monotonically with N.
- Deviations from large-N values are only a few per mille at N=3.
- Scaling and universality are confirmed across lattices.

## Abstract

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 $N=3$.