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 potentialJ(r) parametrized by a Kac-Baker inverse-range parameter γ. The mean-field result is recovered when γ→ 0; in this limit the result is exact. For γ≠ 0, a detailed analysis is given of the phase separation associated with the tricritical point that occurs. The analysis is made through the relation that gives the internal energy viaJ(r). It shows that the MSA result satisfactorily captures the important thermodynamic features of the tricritical point as long as γ is not too large. The case of CoulombicJ(r) is also considered; hereJ(r) is antiferromagnetic. An argument is given in support of the expectation that on the simple cubic and body-centered cubic lattices the CoulombicJ(r) will give rise to a tricritical point at which a λ-line of Néel points meets a paramagnetic-antiferromagnetic coexistence boundary.