  In this article we provide a multitrace analysis of the theory of
noncommutative $\Phi^4$ in two dimensions on the fuzzy sphere ${\bf
S}^2_{N,\Omega}$, and on the Moyal-Weyl plane ${\bf R}^{2}_{\theta, \Omega}$,
with a non-zero harmonic oscillator term added. The doubletrace matrix model
symmetric under $M\longrightarrow -M$ is solved in closed form. An analytical
prediction for the disordered-to-non-uniform-ordered phase transition and an
estimation of the triple point, from the termination point of the critical
boundary, are derived and compared with previous Monte Carlo measurement.
