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We propose a new algorithm for simulating noncommutative phi-four theory onthe fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field,in such a way that in the commutative limit N\longrightarrow \infty, the twomodes decouple and we are left with pure scalar phi-four on the sphere, and ii)diagonalizing the scalar field by means of a U(N) unitary matrix, and thenintegrating out the unitary group from the partition function. The number ofdegrees of freedom in the scalar sector reduces, therefore, from N^2 to the Neigenvalues of the scalar field, whereas the dynamics of the U(1) gauge field,is given by D=3 Yang-Mills matrix model with a Myers term. As an application,the phase diagram, including the triple point, of noncommutative phi-fourtheory on the fuzzy sphere, is reconstructed with small values of N up to N=10,and large numbers of statistics.

New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere