The problem of intermediate valency

The situation is found in a number of rare-earth compounds in which the narrow $f$ level lies near the Fermi level, and configurations of the rare-earth ions differing in the number of $f$ electrons (different valency) have close-lying energies. In this situation many properties of the corresponding substances, both thermodynamic (heat capacity, magnetic susceptibility, compressibility) and kinetic (optical properties, electric conductivity, etc.) are anomalous. Isostructural electronic phase transitions occur in these systems upon changing the external conditions. These are often simultaneously dielectric-metal and magnetic-nonmagnetic transitions. A phase having a narrow resonance level near $E_\mathrm{F}$ has been termed an intermediate-valence (IV) phase. This article reviews generally the problem of intermediate valency. The fundamental experimental facts are summarized. The conditions for appearance and the qualitative picture of IV states are discussed. A table is given of the currently know IV substances. The fundamental theoretical approaches to describing their properties and the electronic phase transitions in these systems are treated. The connection is established with other problems (the problem of dielectric-metal transitions, the Kondo effect, etc.). Major attention is paid to the fundamental unsolved problems.