Spin Pair Correlation Function of Ising Ferromagnet and Antiferromagnet

Abstract

It is shown that the spin pair correlation function of an Ising ferromagnet is calculated from the knowledge of the shift of the magnetization under a presence of an infinitesimal non-uniform field. For the calculation, use is made of the constant coupling approximation, which has been formulated in a form which is applicable to a non-uniform case, by Oguchi and Ono and independently by Morita and Tanaka. The obtained spin pair correlation function for spin 1/2 Ising model is found to be identical to the one which has been obtained by Elliott and Marshall with the aid of the Be the approximation and slightly different from Oguchi and Ono’s result. The obtained spin pair correlation function of the nearest neighbor spins is argued to be in a better approximation than is calculated by the usual constant coupling approximation. The result obtained for a ferromagnet is used to obtain the corresponding result for an Ising antiferromagnet. The formulas are given in a form which is applicable to an arbitrary spin.