  Dynamical mean-field theory is used to study the magnetic instabilities and
phase diagram of the double-exchange (DE) model with Hund's coupling J_H >0 in
infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic
(AF) phases, the DE model supports a broad class of short-range ordered (SRO)
states with extensive entropy and short-range magnetic order. For any site on
the Bethe lattice, the correlation parameter q of a SRO state is given by the
average q=<sin^2(theta_i/2)>, where theta_i is the angle between any spin and
its neighbors. Unlike the FM (q=0) and AF (q=1) transitions, the transition
temperature of a SRO state (T_{SRO}) with 0<q<1 cannot be obtained from the
magnetic susceptibility. But a solution of the coupled Green's functions in the
weak-coupling limit indicates that a SRO state always has a higher transition
temperature than the AF for all fillings p<1 and even than the FM for 0.26\le p
\le 0.39. For 0.39<p<0.73, where both the FM and AF phases are unstable for
small J_H, a SRO phase has a non-zero T_{SRO} except close to p=0.5. As J_H
increases, T_{SRO} eventually vanishes and the FM dominates. For small J_H, the
T=0 phase diagram is greatly simplified by the presence of the SRO phase. A SRO
phase is found to have lower energy than either the FM or AF phases for 0.26\le
p<1. Phase separation (PS) disappears as J_H-->0 but appears for J_H\neq 0. For
p near 1, PS occurs between an AF with p=1 and either a SRO or a FM phase. The
stability of a SRO state at T=0 can be understood by examining the interacting
DOS,which is gapped for any nonzero J_H in an AF but only when J_H exceeds a
critical value in a SRO state.
