  The model of a scalar field with quartic self-interaction on the fuzzy sphere
has three known phases: a uniformly ordered phase, a disordered phase and a
non-uniformly ordered phase, the last of which has no classical counterpart.
These three phases are expected to meet at a triple point. By studying the
infinite matrix size limit, we locate the position of this triple point to
within a small triangle in terms of the parameters of the model. We find the
triple point is closer to the coordinate origin of the phase diagram than
previous estimates but broadly consistent with recent analytic predictions.
