COEXISTENCE OF THE FERROMAGNETIC AND ANTIFERROMAGNETIC LONG-RANGE ORDERS IN THE GENERALIZED ANTIFERROMAGNETIC HEISENBERG-MODEL ON A BIPARTITE LATTICE

The concept of ferrimagnetism was first proposed by Neel to explain wh y some materials have a macroscopic magnetization but no ferromagnetic long-range order, when the temperature T is lower than a phase transi tion temperature T(c). In this article, based on a theorem of Lieb and Mattis, we show in a mathematically rigorous way that the global grou nd states of the generalized antiferromagnetic Heisenberg model on a b ipartite lattice with unequal sublattice points have both ferromagneti c and antiferromagnetic long-range orders with the latter being predom inant. Our rigorous results conform to Neel's theory.