  We investigate the phase structure of a special class of multi-trace
hermitian matrix models, which are candidates for the description of scalar
field theory on fuzzy spaces. We include up to the fourth moment of the
eigenvalue distribution into the multi-trace part of the probability
distribution, which stems from the kinetic term of the field theory action. We
show that by considering different multi-trace behavior in the large moment and
in the small moment regimes of the model, it is possible to obtain a matrix
model, which describes the numerically observed phase structure of fuzzy field
theories. Including the existence of uniform order phase, triple point, and an
approximately straight transition line between the uniform and non-uniform
order phases.
