THE SPIN-ONE ISING-MODEL IN THE MEAN-SPHERICAL APPROXIMATION

The spin-one Ising ferromagnet on a simple cubic lattice is treated in the mean-spherical approximation (MSA) for an exchange potential J(r) parametrized by a Kac-Baker inverse-range parameter gamma, The mean-f ield result is recovered when gamma --> 0; in this limit the result is exact. For gamma not equal 0, a detailed analysis is given of the pha se separation associated with the tricritical point that occurs. The a nalysis is made through the relation that gives the internal energy vi a [J(r)]. it shows that the MSA result satisfactorily captures the imp ortant thermodynamic features of the tricritical point as long as gamm a is not too large. The case of Coulombic J(r) is also considered; her e J(r) is antiferromagnetic, An argument is given in support of the ex pectation that on the simple cubic and body-centered cubic lattices th e Coulombic J(r) will give rise to a tricritical point at which a lamb da-line of Neel points meets a paramagnetic-antiferromagnetic coexiste nce boundary.