  We analyze the phase diagram for a system of weakly-coupled electrons having
an electron- and a hole-band with imperfect nesting. Namely, both bands have
spherical Fermi surfaces, but their radii are slightly different, with a
mismatch proportional to the doping. Such a model is used to describe: the
antiferromagnetism of chromium and its alloys, pnictides, AA-stacked graphene
bilayers, as well as other systems. Here we show that the uniform ground state
of this model is unstable with respect to electronic phase separation in a wide
range of model parameters. Physically, this instability occurs due to the
competition between commensurate and incommensurate antiferromagnetic states
and could be of importance for other models with imperfect nesting.
