  Recently the gaussian expansion method has been applied to investigate the
dynamical generation of 4d space-time in the IIB matrix model, which is a
conjectured nonperturbative definition of type IIB superstring theory in 10
dimensions. Evidence for such a phenomenon, which is associated with the
spontaneous breaking of the SO(10) symmetry down to SO(4), has been obtained up
to the 7-th order calculations. Here we apply the same method to a simplified
model, which is expected to exhibit an analogous spontaneous symmetry breaking
via the same mechanism as conjectured for the IIB matrix model. The results up
to the 9-th order demonstrate a clear convergence, which allows us to
unambiguously identify the actual symmetry breaking pattern by comparing the
free energy of possible vacua and to calculate the extent of ``space-time'' in
each direction.
