  We report a direct and robust calculation, free from ergodic problems, of the
non-uniform-to-uniform (stripe) transition line of noncommutative $\Phi^4_2$ by
means of an exact Metropolis algorithm applied to the first non-trivial
multitrace correction of this theory on the fuzzy sphere. In fact, we
reconstruct the entire phase diagram including the Ising, matrix and stripe
boundaries together with the triple point. We also report that the measured
critical exponents of the Ising transition line agrees with the Onsager values
in two dimensions. The triple point is identified as a termination point of the
one-cut-to-two-cut transition line and is located at
$(\tilde{b},\tilde{c})=(-1.55,0.4)$ which compares favorably with previous
Monte Carlo estimate.
