Fermion determinants in matrix models of QCD at nonzero chemical potential

Journal Article · Wed Oct 01 04:00:00 EDT 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.56.5140· OSTI ID:664910

Halasz, M A ^[1]; Jackson, A D ^[2]; Verbaarschot, J J ^[1]

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1. Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794 (United States)
2. Niels Bohr Institute, Blegdamsvej 17, Copenhagen, DK-2100 (Denmark)

The presence of a chemical potential completely changes the analytical structure of the QCD partition function. In particular, the eigenvalues of the Dirac operator are distributed over a finite area in the complex plane, whereas the zeros of the partition function in the complex mass plane remain on a curve. In this paper we study the effects of the fermion determinant at a nonzero chemical potential on the Dirac spectrum by means of the resolvent G(z) of the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1) model (Gibbs model) and in a random matrix model with the global symmetries of the QCD partition function. In both cases we find that, if the argument z of the resolvent is not equal to the mass m in the fermion determinant, the resolvent diverges in the thermodynamic limit. However, for z=m the resolvent in both models is well defined. In particular, the nature of the limit z{r_arrow}m is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex m and {mu} planes is investigated both by a saddle point approximation and via the distribution of Yang-Lee zeros. Both methods are in complete agreement and lead to a well-defined chiral condensate and quark number density. {copyright} {ital 1997} {ital The American Physical Society}

• Research Organization: New York State University Research Foundation
• DOE Contract Number: FG02-88ER40388
• OSTI ID: 664910
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 8 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHIRAL SYMMETRY
CONDENSATES
DIRAC OPERATORS
EIGENVALUES
FERMIONS
LATTICE FIELD THEORY
PARTITION FUNCTIONS
QUANTUM CHROMODYNAMICS
QUARKS
RANDOMNESS
SPECTRA
U-1 GROUPS