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

TL;DR

This paper derives exact phase diagrams for a complex S=1 kagomé Ising model with multiple interactions by mapping it to a lattice-gas model, revealing rich phase behavior influenced by anisotropy and interactions.

Contribution

It establishes an exact mapping between the S=1 kagomé Ising model and a kagomé lattice-gas model, enabling precise phase diagram determination for the former.

Findings

Phase diagrams show confluent singularities and topology changes.

Phase boundary curves can have positive, negative, or nonmonotonic slopes.

Coexistence curves exhibit diverse shapes and entrapped phases.

Abstract

We consider a S=1 kagom\'e Ising model with triquadratic interactions around each triangular face of the kagom\'e 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 kagom\'e 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 nonmonotonicity, and coexistence curves (magnetization vs temperature) with varying shapes and orientations, in some instances entrapping a homogeneous phase.