Range of order in antiferromagnets with next-nearest neighbor coupling

Abstract

A general argument is presented that a change in the nature of the short-range order will occur above a precisely located temperature TD, the disorder point, for a wide class of magnetic models. The range of order is calculated exactly for two-dimensional asymmetric Ising triangular and union-jack lattices. A sharp cusp in the range of order vs. temperature graph occurs at the disorder point. It is proposed that measurements of the range of order by neutron-diffraction techniques be made on suitable antiferromagnetic crystals to determine whether a disorder point can be detected. It is suggested that two-dimensional antiferromagnets, such as manganese formate dihydrate, may exhibit disorder points.