S=1 kagomé Ising model with triquadratic interactions, single-ion anisotropy and magnetic field: exact phase diagrams

We consider a S=1 kagomé Ising model with triquadratic interactions around each triangular face of the kagomé lattice, single-ion anisotropy and an applied magnetic field. A mapping establishes an equivalence between the magnetic canonical partition function of the model and the grand canonical partition function of a kagomé lattice-gas model with localized three-particle interactions. Since exact phase diagrams are known for condensation in the one-parameter lattice-gas model, the mapping directly provides the corresponding exact phase diagrams of the three-parameter S=1 Ising model. As anisotropy competes with interactions, results include the appearance of confluent singularities effecting changes in the topology of the phase diagrams, phase boundary curves (magnetic field vs. temperature) with purely positive or negative slopes as well as intermediate cases showing non-monotonicity, and coexistence curves (magnetization vs. temperature) with varying shapes and orientations, in some instances entrapping a homogeneous phase.