Operator product expansion on the lattice: a numerical test in the two-dimensional non-linear sigma-model

We consider the short-distance behaviour of the product of the Noether O(N) currents in the lattice nonlinear sigma -model. We compare the numerical results with the predictions of the operator product expansion, using one-loop perturbative renormalization-group improved Wilson coefficients. We find that, even on quite small lattices (m alpha approximate to 1/6), the perturbative operator product expansion describes that data with an error of 5-10% in a large window 2 alpha. less than or similar to x less than or similar to m(-1). We present a detailed discussion of the possible systematic errors.