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The sign problem is a notorious problem, which occurs in Monte Carlosimulations of a system with a partition function whose integrand is notpositive. One way to simulate such a system is to use the factorization methodwhere one enforces sampling in the part of the configuration space which givesimportant contribution to the partition function. This is accomplished by usingconstraints on some observables chosen appropriately and minimizing the freeenergy associated with their joint distribution functions. These observablesare maximally correlated with the complex phase. Observables not in this setessentially decouple from the phase and can be calculated without the signproblem in the corresponding "microcanonical" ensemble. These ideas are appliedon a simple matrix model with very strong sign problem and the results arefound to be consistent with analytic calculations using the Gaussian ExpansionMethod.

Towards an Effective Importance Sampling in Monte Carlo Simulations of a System with a Complex Action