Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature

Details Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature Low-lying Eigenvalues of the QCD Dirac Operator at Finite Temperature

2000-03-24

arxiv.org/abs/hep-lat/0003021v3

Nucl.Phys. B583 (2000) 347-367

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 20 pages, 13 postscript figures. Reference added. To appear in Nucl. Phys. B

Scientific paper

10.1016/S0550-3213(00)00345-X

We compute the low-lying spectrum of the staggered Dirac operator above and below the finite temperature phase transition in both quenched QCD and in dynamical four flavor QCD. In both cases we find, in the high temperature phase, a density with close to square root behavior, $\rho(\lambda) \sim (\lambda-\lambda_0)^{1/2}$. In the quenched simulations we find, in addition, a volume independent tail of small eigenvalues extending down to zero. In the dynamical simulations we also find a tail, decreasing with decreasing mass, at the small end of the spectrum. However, the tail falls off quite quickly and does not seem to extend to zero at these couplings. We find that the distribution of the smallest Dirac operator eigenvalues provides an efficient observable for an accurate determination of the location of the chiral phase transition, as first suggested by Jackson and Verbaarschot.

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