Noncommutativity of the zero chemical potential limit and the thermodynamic limit in finite density systems

Monte Carlo simulations of finite density systems are often plagued by the complex action problem. We point out that there exists certain noncommutativity in the zero chemical potential limit and the thermodynamic limit when one tries to study such systems by reweighting techniques. This is demonstrated by explicit calculations in a Random Matrix Theory, which is thought to be a simple qualitative model for finite density QCD. The factorization method allows us to understand how the noncommutativity, which appears at the intermediate steps, cancels in the end results for physical observables. In the recent reweighting type of approaches to QCD in the small [Formula Presented] regime, we expect a transition when the volume reaches [Formula Presented] which however may not be in the range of current lattice calculations.