  We study the twisted Eguchi-Kawai (TEK) reduction procedure for large-N
unitary matrix lattice models. In particular, we consider the case of
two-dimensional principal chiral models, and use numerical Monte Carlo (MC)
simulations to check the conjectured equivalence of TEK reduced model and
standard lattice model in the large-N limit. The MC results are compared with
the large-N limit of lattice principal chiral models to verify the supposed
equivalence. The consistency of the TEK reduction procedure is verified in the
strong-coupling region, i.e. for $\beta<\beta_c$ where $\beta_c$ is the
location of the large-N phase transition. On the other hand, in the
weak-coupling regime $\beta>\beta_c$, relevant for the continuum limit, our MC
results do not support the equivalence of the large-N limits of the lattice
chiral model and the corresponding TEK reduction. The implications for the
correspondence between TEK model and noncommutative field theory are also
discussed.
