Coexistence of the ferromagnetic and antiferromagnetic long-range orders in the generalized antiferromagnetic Heisenberg model on a bipartite lattice

Abstract

The concept of ferrimagnetism was first proposed by Neel to explain why some materials have a macroscopic magnetization but no ferromagnetic long-range order, when the temperature T is lower than a phase transition temperature Tc. In this article, based on a theorem of Lieb and Mattis, we show in a mathematically rigorous way that the global ground states of the generalized antiferromagnetic Heisenberg model on a bipartite lattice with unequal sublattice points have both ferromagnetic and antiferromagnetic long-range orders with the latter being predominant. Our rigorous results conform to Neel's theory.