Variation of the Critical Temperatures of Ising Antiferromagnets with Applied Magnetic Field

Abstract

High-temperature expansions of the free energy of Ising ferro- and antiferromagnets on the square, simple cubic, and body-centered cubic lattices have been derived directly from the corresponding low-temperature expansions using a generalization of the technique proposed by Domb. These lattices, being loose-packed, can be divided into two identical sublattices, α and β, such that every α site has only β sites as nearest neighbors. The high-temperature expansions treat the finite magnetic fields on the α and β sites as independent quantities. With these series, which extend to eleventh order in the appropriate energies divided by kT, the high-temperature expansions of the staggered susceptibility (the susceptibility with respect to a magnetic field whose sign on the α sites is the negative of its sign on the β sites) has been evaluated for finite applied constant magnetic field. This staggered susceptibility shows a strong singularity at the antiferromagnetic critical temperature, and is analagous to the normal susceptibility of an Ising ferromagnet. The variation of the critical temperature has been obtained numerically for various ratios of the applied magnetic-field energy to the coupling energy using the method of Padé approximants. The results are well described by an expression of the form Tc(H)/Tc(0) = [1 — (H/Hc)2]ξ, with ξ = 0.87, 0.35, and 0.36 for the square, simple cubic, and bcc lattices, respectively. Here, Hc = —zJ/m, where z is the coordination number, J is the spin coupling energy, and m is the magnetic moment.