| Quantum chromodynamics at nonzero baryon density exhibits a complex fermion determinant, giving rise to the sign problem in dynamical Monte Carlo simulations. The severity of the sign problem is captured by the phase of the determinant. Motivated by the equivalence of chiral random matrix theory and QCD to leading order in the epsilon regime we compute the phase of the fermion determinant for general topology in the quenched and unquenched random matrix theory, as a function of the quark chemical potential and the quark mass. The analytic predictions are verified by detailed numerical random matrix simulations. |
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