1997/03/11 by M. A. Halasz, M. Á. Halász, A. D. Jackson +2 · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Complex plane #Dirac operator #Eigenvalues and eigenvectors #Fermion #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Partition function (quantum field theory) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Random Matrices and Applications #Random matrix #Resolvent #Theoretical and Computational Physics #Thermodynamic limit #cond-mat #hep-lat
paper · pdf · doi:10.1103/physrevd.56.5140
published as Phys.Rev.D56:5140-5152,1997 · 27 pages, 6 figures, Latex
arxiv created 1997/03/11 · openalex publication_date 1997/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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\ensuremath→m is illuminated in the Gibbs model. The phase structure of the random matrix model in the complex m and \ensuremathμ 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.