Fermion determinants in matrix models of QCD at nonzero chemical potential

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dc.creatorHalasz, M. A.
dc.creatorJackson, A. D.
dc.creatorVerbaarschot, J. J. M.
dc.date1997-03-11
dc.date.accessioned2026-07-07T11:34:46Z
dc.date.available2026-07-07T11:34:46Z
dc.descriptionThe 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 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 $z \rightarrow m$ is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex m and μ-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.
dc.description27 pages, 6 figures, Latex
dc.identifierhttps://arxiv.org/abs/hep-lat/9703006
dc.identifierhttp://arxiv.org/abs/hep-lat/9703006
dc.identifierPhys.Rev.D56:5140-5152,1997
dc.identifierdoi:10.1103/PhysRevD.56.5140
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/198371
dc.subjectHigh Energy Physics - Lattice
dc.subjectCondensed Matter
dc.titleFermion determinants in matrix models of QCD at nonzero chemical potential
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