Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2001-07-21
Mod.Phys.Lett. A17 (2002) 1355-1365
Physics
Condensed Matter
Disordered Systems and Neural Networks
Version appears in Mod.Phys.Lett.A17(2002)1355
Scientific paper
10.1142/S021773230200779X
In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed there that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall reexamine the multi-flavor or multi-species case rather in detail and argue that the correlator at the band center decays {\em exponentially} for the case of a {\em large} number of flavors. This means that a delocalization-localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studies on multi-flavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behaviour of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD.
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