Determination of the chiral condensate from QCD Dirac spectrum on the lattice

We calculate the chiral condensate of QCD with 2, $2+1$, and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up- and down-quark masses covering a range between 3 and 100 MeV. On L~1.8--1.9 fm lattices at a lattice spacing ~0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined.