Multicomponent spin models with transitive symmetry groups

Some of the multicomponent spin models with transitive symmetry groups derived in the first paper of this series are solved in detail on the Cayley tree pseudo-lattice. The symmetry groups treated are: (i) the group of the cube, L(2)⊗L(4), (ii) the Klein group K(4), equivalent to the Ashkin-Teller model and (iii) the group F(6) as an example of a nonabelian regular permissible group. Three-dimensional phase diagrams in the “ferromagnetic” unit cube are presented for all cases. The connection between the “small-field” Cayley tree phase transitions and those predicted for real lattices by the Bethe approximation is clarified for the general case.