  Recently the complex Langevin method (CLM) has been attracting attention as a
solution to the sign problem, which occurs in Monte Carlo calculations when the
effective Boltzmann weight is not real positive. An undesirable feature of the
method, however, was that it can happen in some parameter regions that the
method yields wrong results even if the Langevin process reaches equilibrium
without any problem. In our previous work, we proposed a practical criterion
for correct convergence based on the probability distribution of the drift term
that appears in the complex Langevin equation. Here we demonstrate the
usefulness of this criterion in two solvable theories with many dynamical
degrees of freedom, i.e., two-dimensional Yang-Mills theory with a complex
coupling constant and the chiral Random Matrix Theory for finite density QCD,
which were studied by the CLM before. Our criterion can indeed tell the
parameter regions in which the CLM gives correct results.
