Random matrix triality at nonzero chemical potential

Journal Article · Mon Dec 01 04:00:00 EST 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.56.7059· OSTI ID:553169

Halasz, M A; Osborn, J C; Verbaarschot, J J ^[1]

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1. Department of Physics, SUNY, Stony Brook, New York 11794 (United States)

We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynamic limit we find that the distribution of the eigenvalues in the complex plane does not depend on the Dyson index, and is given by the solution proposed by Stephanov. For a finite number of degrees of freedom, N, we find an accumulation of eigenvalues on the imaginary axis for real matrices, whereas for quaternion real matrices we find a depletion of eigenvalues in this domain. This effect is of order 1/{radical} (N) . In particular for the real case the resolvent shows a discontinuity of order 1/{radical} (N) . These results are in agreement with lattice QCD simulations with staggered fermions and recent instanton liquid simulations both for two colors and a nonzero chemical potential. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 553169
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 11 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CHIRAL SYMMETRY
COLOR
DIRAC OPERATORS
EIGENVALUES
FERMIONS
INSTANTONS
LATTICE FIELD THEORY
MATRIX ELEMENTS
PARTITION FUNCTIONS
POTENTIALS
QUANTUM CHROMODYNAMICS
RANDOMNESS
SIMULATION