1/N-expansion of the non-linear σ-model: The first three orders

The two-point function of the O(N)-symmetric non-linear σ-model is expanded in 1/N, keeping terms of three leading orders. The mass gap and the magnetic susceptibility obtained from the two-point function are evaluated on square lattices for N=3 and N=4. Using recent high precision Monte Carlo data as bench marks, the systematic error on the truncated 1/N-expansion is smaller than the terms neglected to any of the three orders at hand. Actually, the non-linear σ-model with N≥3 is little more than a Gaussian model in a one-component auxiliary field, as far as the mass gap and magnetic susceptibility are concerned. (orig.)