Exactly soluble Ising models exhibiting multiphase points

A class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins. Within each decorated bond, nearest neighbor ferromagnetic interactions compete with next-nearest neighbor antiferromagnetic interactions. An exact dedecoration transformation reduces the model to an anisotropic Ising model which is exactly soluble in two dimensions (d = 2) and for which accurate series expansion estimates are available for d = 3. Phase diagrams are presented for d = 2 and 3: all exhibit a multiphase point at which many distinct, spatially modulated commensurate phases coexist. The variation of the characteristic wavevector and other properties are compared and contrasted with those of the axial next-nearest neighbor Ising (ANNNI) models.