Constant coupling approximation for Ising spin systems

• Published in: Physica 1956, Vol.22 (1), p.387-396
• Main Author: Kasteleijn, P.W.
• Format: Article
• Language: English
• ISSN: 0031-8914
• DOI: 10.1016/S0031-8914(56)80053-0

The constant coupling approximation for ferro- and antiferromagnetic spin systems with isotropic nearest neighbour interaction, developed in two previous papers, is applied to spin systems with Ising coupling. The partition function of the spin system is expressed in terms of the effective Hamiltonian H e of a pair of neighbouring spins. In the ferromagnetic case, H e contains only an effective Ising coupling term and an effective field term. In the antiferromagnetic case, H e contains in addition a staggered effective field term. The constant coupling approximation which is obtained by assuming that the effective Ising coupling is constant is shown to be equivalent to the familiar quasi-chemical approximation. For an antiferromagnetic spin system with an external field of arbitrary magnitude in the preferred direction this approximation is worked out in detail. Both for the paramagnetic and for the antiferromagnetic phase the thermodynamic quantities of the system are obtained from a basic equation that is analogous to the Bethe-Peierls equation for the ferromagnetic case. The critical data are evaluated, and an explicit formula is derived for the critical curve in the B vs T plane.