January 25, 1994
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(\beta^{10}) 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 $\beta$ and $\gamma$ 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 $N \ge 10$ and the large N physics is well described by a ``hadronization'' picture.
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