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Register a new userMixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on Bethe lattice
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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.
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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.
The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved with the help of decoration-iteration transformation and exact recursion relations. It is shown that the model under investigation exhibits reentrant phase transitions whenever a sufficiently high coordination number of the underlying Bethe lattice is considered.
A bipartite entanglement between two nearest-neighbor Heisenberg spins of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is quantified using a concurrence. It is shown that the concurrence equals zero in a classical ferromagnetic and a quantum disordered phase, while it becomes sizable though unsaturated in a quantum ferromagnetic phase. A thermally-assisted reentrance of the concurrence is found above a classical ferromagnetic phase, whereas a quantum ferromagnetic phase displays a striking cusp of the concurrence at a critical temperature.
Mixed-spin Ising model on a decorated Bethe lattice is rigorously solved by combining the decoration-iteration transformation with the method of exact recursion relations. Exact results for critical lines, compensation temperatures, total and sublattice magnetizations are obtained from a precise mapping relationship with the corresponding spin-1/2 Ising model on a simple (undecorated) Bethe lattice. The effect of next-nearest-neighbour interaction and single-ion anisotropy on magnetic properties of the ferrimagnetic model is investigated in particular. It is shown that the total magnetization may exhibit multicompensation phenomenon and the critical temperature vs. the single-ion anisotropy dependence basically changes with the coordination number of the underlying Bethe lattice. The possibility of observing reentrant phase transitions is related to a high enough coordination number of the underlying Bethe lattice.
The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin-1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered-disordered ground state, which manifest itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behaviour including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.
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