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The geometrically frustrated spin-1/2 Ising-Heisenberg model on triangulated Husimi lattices is exactly solved by combining the generalized star-triangle transformation with the method of exact recursion relations. The ground-state and finite-temperature phase diagrams are rigorously calculated along with both sublattice magnetizations of the Ising and Heisenberg spins. It is evidenced that the Ising-Heisenberg model on triangulated Husimi lattices with two or three inter-connected triangles-in-triangles units displays in a highly frustrated region a quantum disorder irrespective of temperature, whereas the same model on triangulated Husimi lattices with a greater connectivity of triangles-in-triangles units exhibits at low enough temperatures an outstanding quantum order due to the order-by-disorder mechanism. The quantum reduction of both sublattice magnetizations in the peculiar quantum ordered state gradually diminishes with increasing the coordination number of underlying Husimi lattice.

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Abstract:The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial singleion anisotropy terms is solved exactly 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. 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.PACS (

The relaxation behaviour of the Blume-Emery-Griffiths (BEG) model Hamiltonian with bilinear and biquadratic nearest-neighbour ferromagnetic exchange interaction and crystal field interactions is studied by using the molecular field approximation (MFA) and Onsager's theory of irreversible thermodynamics. First the equilibrium behaviour and the phase diagrams of the model in MFA are given briefly in order to understand the relaxation behaviour. Then, Onsager theory is applied to the model and the set of linear differential equations, which is also called the kinetic or rate equations, is obtained. By solving these equations a set of relaxation times is calculated and examined for temperatures near the critical and multicritical points. It is found that one of the relaxation times 1 ( ) τ is sharply cusped at the triple and critical points, whereas it approaches infinity near the critical-end point. On the other hand, the other relaxation time 2 ( ) τ displays a jump-discontinuity behaviour at the triple and critical points but it has a cusp at the critical-end point. A maximum of 2 τ has also been observed above the critical-end point. Moreover, similar calculations are performed for non-zero magnetic field (H) to investigate the effect of H on relaxation times.