  The matrix model formulation of superstring theory offers the possibility to
understand the appearance of 4d space-time from 10d as a consequence of
spontaneous breaking of the SO(10) symmetry. Monte Carlo studies of this issue
is technically difficult due to the so-called sign problem. We present a
practical solution to this problem generalizing the factorization method
proposed originally by two of the authors (K.N.A. and J.N.). Explicit Monte
Carlo calculations and large-N extrapolations are performed in a simpler matrix
model with similar properties, and reproduce quantitative results obtained
previously by the Gaussian expansion method. Our results also confirm that the
spontaneous symmetry breaking indeed occurs due to the phase of the fermion
determinant, which vanishes for collapsed configurations. We clarify various
generic features of this approach, which would be useful in applying it to
other statistical systems with the sign problem.
