Sublattice-ordered phases of Griffiths’s three-component model

We describe the essential features of the mean-field phase diagram for the spin-1 Ising model with general nearest-neighbor interaction when sublattice ordering is made explicit. The phase diagram (in five-dimensional field space) can be classified into 84 zones where uniform with ordered phase coexistence is identified and multicritical behavior is determined. This generalized Ising model was studied extensively, in its ferromagnetic version, by Furman, Dattagupta, and Griffiths towards the end of the last decade. Here we complement that study with the antiferromagnetic phase behavior associated with the same model. Two different mappings between uniform and ordered phase existence conditions facilitated our task and indicated the interconnections that exist between ferromagnetic and antiferromagnetic properties in the model. Known features, like the ``shield'' region, appear reproduced in other energy-parameter locations, but also new features occur, such as additional tricritical and fourth-order critical lines connected by sixth-order critical points.