We study a two parameter single trace 3-matrix model with SO(3) global
symmetry. The model has two phases, a fuzzy sphere phase and a matrix phase.
Configurations in the matrix phase are consistent with fluctuations around a
background of commuting matrices whose eigenvalues are confined to the interior
of a ball of radius R=2.0. We study the co-existence curve of the model and
find evidence that it has two distinct portions one with a discontinuous
internal energy yet critical fluctuations of the specific heat but only on the
low temperature side of the transition and the other portion has a continuous
internal energy with a discontinuous specific heat of finite jump. We study in
detail the eigenvalue distributions of different observables.Comment: 20 page
