A Multitrace Approach to Noncommutative \Phi_2^4

In this article we provide a multitrace analysis of the theory of noncommutative ${\mathrm{\Phi }}^4$ in two dimensions on the fuzzy sphere ${\bf S}^2_{N,\Omega}$,andontheMoyal-Weylplane${\bf R}^{2}_{\theta, \Omega}$, with a non-zero harmonic oscillator term added. The doubletrace matrix model symmetric under $M⟶-M$ 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.