  We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3)
mass terms based on the cohomological approach and the Monte Carlo method. In
the bosonic models we show the existence of an exotic first/second order
transition from a phase with a well defined background geometry (the fuzzy
sphere) to a phase with commuting matrices with no geometry in the sense of
Connes. At the transition point the sphere expands abruptly to infinite size
then it evaporates as we increase the temperature (the gauge coupling
constant). The transition looks first order due to the discontinuity in the
action whereas it looks second order due to the divergent peak in the specific
heat. The fuzzy sphere is stable for the supersymmetric models in the sense
that the bosonic phase transition is turned into a very slow crossover
transition. The transition point is found to scale to zero with N. We
conjecture that the transition from the background sphere to the phase of
commuting matrices is associated with spontaneous supersymmetry breaking. The
eigenvalues distribution of any of the bosonic matrices in the matrix phase is
found to be given by a non-polynomial law obtained from the fact that the joint
probability distribution of the four matrices is uniform inside a solid ball
with radius R. The eigenvalues of the gauge field on the background geometry
are also found to be distributed according to this non-polynomial law. We also
discuss the D=3 models and by using cohomological deformation, localization
techniques and the saddle-point method we give a derivation of the D=3
eigenvalues distribution starting from a particular D=4 model.
