We analyze a family of one and bi-dimensional frustrated Heisenberg systems, whose ground state ͑GS͒ and low lying excitation spectrum can be exactly described as a product. The magnetic lattice is composed by clusters of spin S ions. These clusters are connected to each other by intermediate, spin ions ͑here called "connectors"͒. The value of S and are arbitrary. Three major properties of these systems are: ͑i͒ The GS is exponentially degenerate. ͑ii͒ The low lying excitations are separated from the GS by a gap, and they are localized. However, neighbor excitations interact, exchanging energy; two "bottom" excitations repel each other. ͑iii͒ The magnetization curve has a staircaselike form. On introducing a direct connector-connector coupling, a break in the lattice translational symmetry can occur, due to the uniform magnetic field. Finally, we study the effect of a weak departure from the hypothesis of the model, with the aim to make it more adaptable to fit different actual magnetic systems. We obtain bands of delocalized excitations. Bounded states between excitations also appear.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.