Phase of the Fermion Determinant at Nonzero Chemical Potential

Abstract

We show that in the microscopic domain of QCD (also known as the $\hat{I}\mu$-domain) at nonzero chemical potential the average phase factor of the fermion determinant is nonzero for $\hat{I}¼<m_{\ddot{I}}€/2$ and is exponentially suppressed for larger values of the chemical potential. This follows from the chiral Lagrangian that describes the low-energy limit of the expectation value of the phase factor. Explicit expressions for the average phase factor are derived using a random matrix formulation of the zero momentum limit of this chiral Lagrangian.

4 pages, 1 figure