On the phase structure of QCD with Wilson fermions

The phase structure of lattice QCD with Wilson fermions is discussed. Analytic and numerical evidences are given for the spontaneous breaking of parity and flavor symmetry, which naturally explains the existence of the massless pion at the critical hopping parameter $K_c$ without recourse to the chiral symmetry absent in the Wilson fermion formulation. New numerical evidences are also presented for the multiple structure of the critical lines in the weak coupling region. A connection between the phase structure and the finite temperature phase transition is briefly mentioned.