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Register a new userS=1 kagome Ising model with triquadratic interactions, single-ion anisotropy and magnetic field: exact phase diagrams
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We consider a S=1 kagome Ising model with triquadratic interactions around each triangular face of the kagome 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 kagome 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.
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The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is exactly solved by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams and compensation phenomenon) are investigated in detail. The particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.
We analyze the gaps in the excitation spectrum of a Haldane chain with single-ion anisotropy in a staggered field. We show that the gap along the direction of the field increases at a faster rate than the others, while its spectral weight decreases, being transferred to a two-magnon continuum.
The field-induced transition in one-dimensional S=1 Heisenberg antiferromagnet with single-ion anisotropy in the presence of a transverse magnetic field is obtained on the basis of the Schwinger boson mean-field theory. The behaviors of the specific heat and susceptibility as functions of temperature as well as the applied transverse field are explored, which are found to be different from the results obtained under a longitudinal field. The anomalies of the specific heat at low temperatures, which might be an indicative of a field-induced transition from a Luttinger liquid phase to an ordered phase, are explicitly uncovered under the transverse field. A schematic phase diagram is proposed. The theoretical results are compared with experimental observations.
Ground states of the frustrated spin-1 Ising-Heisenberg two-leg ladder with Heisenberg intra-rung coupling and only Ising interaction along legs and diagonals are rigorously found by taking advantage of local conservation of the total spin on each rung. The constructed ground-state phase diagram of the frustrated spin-1 Ising-Heisenberg ladder is then compared with the analogous phase diagram of the fully quantum spin-1 Heisenberg two-leg ladder obtained by density matrix renormalization group (DMRG) calculations. It is demonstrated that both investigated spin models exhibit quite similar magnetization scenarios, which involve intermediate plateaux at one-quarter, one-half and three-quarters of the saturation magnetization.
Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d=3 physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers, are obtained for Ising, XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.
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