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The La 1−x Sr x MnO 3 system with 0.2 x 0.4 has traditionally been modelled with a "double exchange" Hamiltonian, in which it is assumed that the only relevant physics is the tendency of carrier hopping to line up neighboring spins. We present a solution of the double exchange model, show it is incompatible with many aspects of the resistivity data, and propose that a strong electron-phonon interaction arising from a Jahn-Teller splitting of the outer Mn d-level plays a crucial role.

A phenomenological model of a system of antiferromagnetically correlated spins is shown to give a good quantitative description of NMR, nuclear-quadrupole-resonance, and Knight-shift measurements on yttrium, planar copper, and planar oxygen sites in YBa2Cu307. The antiferromagnetic correlation length is estimated to be -2.5 lattice constants at T =100 K. The temperature dependence of the correlation length ceases at T"=100K. The enhancement of the observed relaxation rates over what is expected for weakly interacting electrons is calculated and shown to be large. Extension of the calculation to other cuprate superconductors is discussed.Fermi liquid, the spin-lattice relaxation rate, 8' has the Korringa temperature dependence O'-T. This temperature dependence may be understood as follows: for a Fermi liquid the density of states for spin cxcitations is constant at low energies. The rate is given by the number of thermally excited spin excitations, which in this case scales as T. In the high-T, cuprate superconductors, the Cu relaxation rate 8' varies more slowly than the Korringa rate for T& T*. The crossover temperature T* 42

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We calculate the fermion Green function and particle-hole susceptibilities for a degenerate twodimensional fermion system with a singular gauge interaction. We show that this is a strong coupling problem, with no small parameter other than the fermion spin degeneracy, N. We consider two interactions, one arising in the context of the t − J model and the other in the theory of half-filled Landau level. For the fermion self energy we show in contrast to previous claims that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility χQ at a general wavevector Q = 2pF retains the fermi-liquid form. However the 2pF susceptibility χ2p F either diverges as T → 0 or remains finite but with nonanalytic wavevector, frequency and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d = 2, but irrelevant at low energies in d ≥ 2.