A bstract We propose a new algorithm for simulating noncommutative phi-four theory on the 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 → ∞, the two modes 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 then integrating out the unitary group from the partition function. The number of degrees of freedom in the scalar sector reduces, therefore, from N _(2)to the N eigenvalues 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-four theory on the fuzzy sphere, is reconstructed with small values of N up to N = 10, and large numbers of statistics.
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