Two dimensional SU(N) x SU(N) chiral models on the lattice

Lattice $SU(N)\times SU(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. $12^{th}$ order strong coupling series for the free and internal energy are obtained for all $N\geq 6$. Three loop contributions to the internal energy and to the lattice $\beta$-function are evaluated for all $N$ and non-universal corrections to the asymptotic $\Lambda$ parameter are computed in the ``temperature'' and the ``energy'' scheme. Numerical simulations confirm a faster approach to asymptopia of the energy scheme. A phenomenological correlation between the peak in the specific heat and the dip of the $\beta$-function is observed. Tests of scaling are performed for various physical quantities, finding substantial scaling at $\xi \gtrsim 2$. In particular, at $N=6$ three different mass ratios are determined numerically and found in agreement, within statistical errors of about 1\%, with the theoretical predictions from the exact S-matrix theory.