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

Abstract

Lattice $\mathrm{SU}(N)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(N)$ chiral models are analyzed by strong and weak coupling expansions and by numerical simulations. Twelfth-order strong coupling series for the free and internal energy are obtained for all $N\ensuremath{\ge}6$. Three-loop contributions to the internal energy and to the lattice $\ensuremath{\beta}$ function are evaluated for all $N$ and nonuniversal corrections to the asymptotic $\ensuremath{\Lambda}$ parameter are computed in the "temperature" and the "energy" schemes. 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 $\ensuremath{\beta}$ function is observed. Tests of scaling are performed for various physical quantities, finding substantial scaling at $\ensuremath{\xi}\ensuremath{\gtrsim}2$. 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.