LOCALIZED MAGNETIC MODELS WITH HIGHER-ORDER INTERACTIONS

Investigation of the higher-order exchange interactions in magnetic spin systems has received during last decades increasing attention. In fact, many experimental studies have recently reported physical phenomena that cannot be explained using the standard approach based on theoretical models with pair interactions only. For this reason a lot of effort has been directed to the development theoretical models that may account for higher-order interaction energy terms. In this work we extensively review recent development in this interesting research field with the special emphasis on the works dealing with magnetic systems with higher-order spin interactions. A special attention is payed to the classification of the four-spin interactions that play an important role in magnetic spin systems. The substantial part of this contribution deals with the review of recent theoretical results obtained for various exactly solvable mixed-spin Ising models on decorated lattices. The particular attention is directed to understanding the influence of a special kind of higher-order interaction which is usually called as a three-site four-spin interaction. This interaction among other interesting physical effects also reveals a possible link between higher-order spin interactions and magneto-elastic properties of various real magnetic compound.