COMPARISON BETWEEN THEORETICAL 4-LOOP PREDICTIONS AND MONTE-CARLO CALCULATIONS IN THE 2-DIMENSIONAL N-VECTOR MODEL FOR N=3,4,8

We have computed the four-loop contribution to the beta-function and t o the anomalous dimension of the field for the two-dimensional lattice N-vector model. This allows the determination of the second perturbat ive correction to various long-distance quantities like the correlatio n lengths and the susceptibilities. We compare these predictions with new Monte Carlo data for N = 3, 4, 8. From these data we also extract the values of various universal nonperturbative constants, which we co mpare with the predictions of the 1/N expansion.