  We show, using the periodic Anderson model, that the local spin self-energy
approximation, as implemented in the extended dynamical mean field theory
(EDMFT), results in a first order phase transition which persists to T=0.
Around the transition, there is a finite coexistence region of the paramagnetic
and antiferromagnetic (AFM) phases. The region is bounded by two critical
transition lines which differ by an electron-hole bubble at the AFM ordering
wave vector.
