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The IIB matrix model proposes a mechanism for dynamically generating fourdimensional space--time in string theory by spontaneous breaking of the tendimensional rotational symmetry $\textrm{SO}(10)$. Calculations using theGaussian expansion method (GEM) lend support to this conjecture. We study asimple $\textrm{SO}(4)$ invariant matrix model using Monte Carlo simulationsand we confirm that its rotational symmetry breaks down, showing that lowerdimensional configurations dominate the path integral. The model has a strongcomplex action problem and the calculations were made possible by the use ofthe factorization method on the density of states $\rho_n(x)$ of properlynormalized eigenvalues $\tilde\lambda_n$ of the space--time moment of inertiatensor. We study scaling properties of the factorized terms of $\rho_n(x)$ andwe find them in agreement with simple scaling arguments. These can be used inthe finite size scaling extrapolation and in the study of the region ofconfiguration space obscured by the large fluctuations of the phase. Thecomputed values of $\tilde\lambda_n$ are in reasonable agreement with GEMcalculations and a numerical method for comparing the free energy of thecorresponding ansatze is proposed and tested.

A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method