The Aoki phase for N f = 2 Wilson fermions revisited ∗

In studies of chiral symmetry breaking it is desirable to start from an (almost) chirally invariant formulation of lattice fermions. At present this is best realized by using fermions satisfying the Ginsparg-Wilson relation, e.g. using the overlap operator, or by working with the domain wall framework [1]. In such approaches Wilson fermions are still important as an input. For the Wilson-Dirac operator (which breaks chiral invariance explicitly) in Nf = 2 lattice QCD Aoki [2] has predicted that in a certain parameter range there is a phase in which parity and flavor symmetry are both spontaneously broken. It is separated from an unbroken phase by a line of second order phase transition on which the pion states are expected to become massless [3]. In Fig. 1 the proposed phase diagram is sketched in the (β, κ)-plane . In a recent paper [4] it has been pointed out that the features of the Aoki phase are of relevance for locality and for restoration of chiral invariance in quenched and full QCD with Ginsparg-Wilson and domain wall fermions. Accordingly, the region of the Aoki phase has to be avoided in such investigations in order not to spoil physical reliability. In the light of this it is important to have precise information about the region where the Aoki phase really occurs. In the past it has been ques-