A Multitrace Approach to Noncommutative Φ_2^4

Abstract: 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.