  Using dynamical mean-field theory, we have evaluated the magnetic
instabilities and T=0 phase diagram of the double-exchange model on a Bethe
lattice in infinite dimensions. In addition to ferromagnetic (FM) and
antiferromagnetic (AF) phases, we also study a class of disordered phases with
magnetic short-range order (SRO). In the weak-coupling limit, a SRO phase has a
higher transition temperature than the AF phase for all fillings p below 1 and
can even have a higher transition temperature than the FM phase. At T=0 and for
small Hund's coupling J_H, a SRO state has lower energy than either the FM or
AF phases for 0.26\le p < 1. Phase separation is absent in the J_H --> 0 limit
but appears for any non-zero value of J_H.
