Perturbative calculation of the spin-wave dispersion in a disordered   double-exchange model
  We study the spin-wave dispersion of localized spins in a disordered double-exchange model using the perturbation theory with respect to the strength of the disorder potential. We calculate the dispersion upto the next-leading order, and extensively examine the case of one-dimension. We show that in that case, disorder yields anomalous gapped-like behavior at the Fermi wavenumber of the conduction electrons. 
T. Semba and T. Fukui