Two-dimensional SU(N)xSU(N) chiral models on the lattice. II. The Green's function

Analytical and numerical methods are applied to principal chiral models on a two-dimensional lattice and their predictions are tested and compared. New techniques for the strong coupling expansion of SU(N) models are developed and applied to the evaluation of the two-point correlation function. The momentum-space lattice propagator is constructed with precision O(β10) and an evaluation of the correlation length is obtained for several different definitions. Three-loop weak coupling contributions to the internal energy and to the lattice β and γ functions are evaluated for all N, and the effect of adopting the ''energy'' definition of temperature is computed with the same precision. Renormalization-group-improved predictions for the two-point Green's function in the weak coupling (continuum) regime are obtained and successfully compared with Monte Carlo data. We find that strong coupling is predictive up to a point where asymptotic scaling in the energy scheme is observed. Continuum physics is insensitive to the effects of the large N phase transition occurring in the lattice model. Universality in N is already well established for N approx-gt 10 and the large N physics is well described by a ''hadronization'' picture