  Lattice QCD with two flavors of Wilson fermions can exhibit spontaneous
breaking of flavor and parity, with the resulting "Aoki phase" characterized by
the non-zero expectation value $<\bar\psi \gamma_5 \tau_3 \psi>\ne0$. This
phenomenon can be understood using the chiral effective theory appropriate to
the Symanzik effective action. Within this standard analysis, the
flavor-singlet pseudoscalar expectation value vanishes: $<i \bar\psi \gamma_5
\psi>=0$. A recent reanalysis has questioned this understanding, arguing that
either the Aoki-phase is unphysical, or that there are additional phases in
which $<i \bar\psi \gamma_5 \psi>\ne0$. The reanalysis uses the properties of
probability distribution functions for observables built of fermion fields and
expansions in terms of the eigenvalues of the hermitian Wilson-Dirac operator.
Here I show that the standard understanding of the Aoki-phase is, in fact,
consistent with the approach used in the reanalysis. Furthermore, if one
assumes that the standard understanding is correct, one can use the methods of
the reanalysis to derive lattice generalizations of the continuum sum rules of
Leutwyler and Smilga.
