  The low-energy effective theory of the IIB matrix model developed by H. Aoki
et al. is written down explicitly in terms of bosonic variables only. The
effective theory is then studied by Monte Carlo simulations in order to
investigate the possibility of a spontaneous breakdown of Lorentz invariance.
The imaginary part of the effective action, which causes the so-called sign
problem in the simulation, is dropped by hand. The extent of the eigenvalue
distribution of the bosonic matrices shows a power-law large N behavior,
consistent with a simple branched-polymer prediction. We observe, however, that
the eigenvalue distribution becomes more and more isotropic in the
ten-dimensional space-time as we increase N. This suggests that if the
spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix
model, a crucial role must be played by the imaginary part of the effective
action.
