Abstract
Dyson-Schwinger equations for the O( N)-symmetric non-linear σ-model are derived and expanded in 1 N . A closed set of equations is obtained by keeping only the leading term and the first correction term in this expansion. These equations are solved numerically in two dimensions on square lattices of sizes 50×50 and 100×100. Results for the magnetic susceptibility and the mass gap are compared with predictions of the ordinary 1 N - expansion and with Monte Carlo results. The results obtained with the Dyson-Schwinger equations show the same scaling behavior as found in the Monte Carlo results. This is not the behavior predicted by the perturbative renormalization group.
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