  We study the phase structure of the four-dimensional twisted Eguchi-Kawai
model using numerical simulations. This model is an effective tool for studying
SU(N) gauge theory in the large-N limit and provides a nonperturbative
formulation of the gauge theory on noncommutative spaces. Recently it was found
that its Z_N^4 symmetry, which is crucial for the validity of this model, can
break spontaneously in the intermediate coupling region. We investigate in
detail the symmetry breaking point from the weak coupling side. Our simulation
results show that the continuum limit of this model cannot be taken.
