Magnetic Susceptibility of the Double-Exchange Model in the RKKY Limit

The magnetic susceptibility and Edwards-Anderson order parameter q of the spin-glass-like (SGL) phase of the double-exchange model are evaluated in the weak-coupling or RKKY limit. Dynamical mean-field theory is used to show that q=M(T/Tsg)^2, where M is the classical Brillouin function and Tsg is the SGL transition temperature. The correlation length of the SGL phase is determined by a correlation parameter Q that maximizes Tsg and minimizes the free energy. The magnetic susceptibility has a cusp at Tsg and reaches a nonzero value as T goes to zero.