SPONTANEOUS FLAVOR AND PARITY BREAKING WITH WILSON FERMIONS - ART. NO. 074501

We discuss the phase diagram of Wilson fermions in the m(0)-g(2) plane for two-flavor QCD. We argue that, as originally suggested by Aoki, t here is a phase in which flavor and parity are spontaneously broken. R ecent numerical results on the spectrum of the overlap Hamiltonian hav e been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity brok en ''Aoki phase.'' We also show how, as the continuum limit is approac hed, one can study the lattice theory using the continuum chiral Lagra ngian supplemented by additional terms proportional to powers of the l attice spacing. We find that there are two possible phase structures a t non-zero lattice spacing: (1) there is an Aoki phase of width Delta m(0) similar to a(3) with two massless Goldstone pions: (2) there is n o symmetry breaking, and all three pions have an equal non-vanishing m ass of order a. Present numerical evidence suggests that the former op tion is realized for Wilson fermions. Our analysis then predicts the f orm of the pion masses and the flavor-parity breaking condensate withi n the Aoki phase. Our analysis also applies for non-perturbatively imp roved Wilson fermions. [S0556-2821(98)06817-9].