  The sign problem is a notorious problem, which occurs in Monte Carlo
simulations of a system with a partition function whose integrand is not
positive. One way to simulate such a system is to use the factorization method
where one enforces sampling in the part of the configuration space which gives
important contribution to the partition function. This is accomplished by using
constraints on some observables chosen appropriately and minimizing the free
energy associated with their joint distribution functions. These observables
are maximally correlated with the complex phase. Observables not in this set
essentially decouple from the phase and can be calculated without the sign
problem in the corresponding "microcanonical" ensemble. These ideas are applied
on a simple matrix model with very strong sign problem and the results are
found to be consistent with analytic calculations using the Gaussian Expansion
Method.
