ANALYTICAL APPROACH TO THE HEISENBERG-ANTIFERROMAGNET WITH NEAREST-NEIGHBOR AND NEXT-NEAREST-NEIGHBOR EXCHANGE

We investigate the ground-state energy of a two-dimensional Heisenberg antiferromagnet with competing nearest-and next-nearest-neighbor exch ange interactions J(1) and J(2). On the basis of a recently introduced cumulant technique we describe the transition from the usual antiferr omagnetic phase to a so-called layered antiferromagnetic phase as a fu nction of the ratio J(2)/J(1). Whereas in the former phase the spins a re approximately aligned antiparallel along the up and down sublattice , in the layered phase each of the two sublattices forms an antiferrom agnetic lattice by itself. The result for the round-state energy and f or respective order parameters agree well with findings obtained from numerical methods.