Cooperative phenomena in strongly correlated electron systems

In this review we present results of our theoretical study of cooperative phenomena in strongly correlated electron systems obtained within various generalizations of the Falicov-Kimball model. The primary goal of this study was to identify crucial interactions that lead to the stabilization of the specific cooperative phenomenon, and then try to elaborate its comprehensive microscopic description. The main attention is devoted to a discussion of valence and metal-insulator transitions, formation of charge and spin ordering, electronic ferroelectricity, itinerant ferromagmetism and mechanisms leading to their stabilization. Among the major mechanisms we examine the effect of local and nonlocal Coulomb interaction between localized and itinerant electrons, local and nonlocal hybridization, long-range and correlated hopping of itinerant electrons and spin-dependent interaction between localized and itinerant electrons, both for zero and nonzero temperatures, as well as for doped and undoped systems. Finally, the relevance of resultant solutions for a description of rare-earth and transition-metal compounds is discussed (Author)