Magnetic properties are calculated for a spin one-half Heisenberg ferromagnet in which the exchange interactions deviate randomly in strength from the mean interaction,, Disorder produces a low-energy peak and a high-energy tail in the density of spin-wave states for a simple-cubic geometry. The ferromagnetic Curie temperature is shown to decrease linearly with disorder; the temperature-dependent magnetization is not otherwise markedly altered.

A theory of the collective electronic states of linear-chain molecular crystals is developed. The theory is applicable to cases where the intermolecular electronic interaction is so strong that the electronic structures of the molecules in the crystal lattice may be grossly different from the electronic structures of the isolated molecules. Strong intermolecular interactions due to (a) dispersion forces and (b) intermolecular charge transfer, are considered. Case (a) corresponds to an extension of the Davydov singlet exciton theory to cases where the first-order exciton bandwidth is comparable to, or greater than, the isolated-molecule excitation energy. New features emerge in this strong coupling region, such as low exciton excitation energies, and ferroelectric-type electronic polarization. Case (b) represents an extension of Mulliken's theory of intermolecular charge transfer to infinite chains of alternating donor and acceptor molecules. The cooperative aspects of the intermolecular charge transfer are included using a Hartree-like self-consistent field approximation. The energy gap for charge-carrying elementary excitations is calculated. The calculations are also applicable to the problem of intermolecular charge transfer and electrical conductivity in regular linear molecular chains of N molecules and N/2 mobile electrons.