We use a many-body coherent potential approximation (CPA) to study the para
magnetic state of the double exchange model with finite local spins S. Our
CPA treats dynamical effects due to the quantum nature of the local spins i
n a local approximation, becomes exact in the atomic limit. and reduces to
Kubo's one-electron CPA in the empty band limit and to dynamical mean field
theory (DMFT) in the classical S --> infinity limit. We solve the CPA equa
tions of motion for all S in the strong Hund coupling limit, determining al
l quantities self-consistently, We show that the CPA does not give a Ferrom
agnetic transition for any S; this is due to the local spin probability dis
tribution Function P(S-z) being inaccurately obtained. We bypass this diffi
culty by extrapolating P(S-z) From the exact (within DMFT)S = infinity resu
lt, and obtain a magnetic transition for all S with the expected Curie laws
at band filling n = 0, 1. (C) 2000 Elsevier Science B.V. All rights reserv
ed.