  We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge
background given by an Instanton Liquid Model (ILM) at temperatures around the
chiral phase transition. For two massless quark flavors we observe that at the
chiral phase transition, both the low lying eigenmodes and the spectrum of the
QCD Dirac operator resemble those of a disordered conductor at the Anderson
transition. In particular we present results showing that the eigenvectors are
multifractal and the spectral correlations are well described by critical
statistics. We also find an additional temperature dependent mobility edge
located in the bulk of the spectrum with properties quantitatively similar to
those of a 3D disordered conductor at the Anderson transition. This feature is
present in both quenched and unquenched simulations. Finally we argue that our
findings are not in principle restricted to the ILM approximation and may also
be found in lattice simulations.
