Abstract
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.
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