We rewrite Z = Z+ - Z- , where Z+ and Z- have good positivity properties, and conjecture, based on arguments using the analytic properties of the free energy, that at most points of the phase diagram Z+ dominates Z-. At such points one can simulate the theory using Monte Carlo.
http://arxiv.org/abs/0808.2987 (paper available after 5 pm pacific 8.24.08)
Sign problem? No problem -- a conjecture
Stephen D.H. Hsu, David Reeb
We investigate the Euclidean path integral formulation of QCD at finite baryon density. We show that the partition function Z can be written as the difference between two sums, each of which defines a partition function with positive weights. We argue that at most points on the phase diagram one will give an exponentially larger contribution than the other. At such points Z can be replaced by a more tractable path integral with positive definite measure, allowing for lattice simulation as well as the application of QCD inequalities. We also propose a test to control the accuracy of approximation in actual Monte Carlo simulations. Our analysis may be applicable to other systems with a sign problem, such as chiral gauge theory.