A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration-iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined.

An exactly solvable variant of mixed spin-(1/2,1) Ising-Heisenberg diamond chain is considered. Vertical spin-1 dimers are taken as quantum ones with Heisenberg bilinear and biquadratic interactions and with single-ion anisotropy, while all interactions between spin-1 and spin-1/2 residing on the intermediate sites are taken in the Ising form. The detailed analysis of the T = 0 ground state phase diagram is presented. The phase diagrams have shown to be rather rich, demonstrating large variety of ground states: saturated one, three ferrimagnetic with magnetization equal to 3/5 and another four ferrimagnetic ground states with magnetization equal to 1/5. There are also two frustrated macroscopically degenerated ground states which could exist at zero magnetic filed. Solving the model exactly within classical transfer-matrix formalism we obtain an exact expressions for all thermodynamic function of the system. The thermodynamic properties of the model have been described exactly by exact calculation of partition function within the direct classical transfer-matrix formalism, the entries of transfer matrix, in their turn, contain the information about quantum states of vertical spin-1 XXZ dimer (eigenvalues of local hamiltonian for vertical link). *

We propose the general scheme of incorporation of the Dirac monopoles into mechanical systems on the three-dimensional conformal flat space. We found that any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates can be extended to the integrable system with the Dirac monopoles located at the foci of the corresponding coordinate systems. Particular cases of this class of system are the two-center MICZ-Kepler system in the Euclidean space, the limiting case when one of the background dyons is located at the infinity as well as the model of particle in parabolic quantum dot in the presence of parallel constant uniform electric and magnetic fields.

The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground state properties are also investigated, the corresponding ground state phase diagram is presented.

We calculate the entropy and cooling rate of the antiferromagnetic spin-1/2 XXZ chain under an adiabatic demagnetization process using the quantum transfer-matrix technique and non-linear integral equations. The limiting case of the Ising chain (corresponding to infinitely large anisotropy) is presented for comparison. Our exact results for the Heisenberg chain are used as a crosscheck for the numerical exact diagonalization as well as Quantum Monte Carlo simulations and allow us to benchmark the numerical methods. Close to field-induced quantum phase transitions we observe a large magnetocaloric effect. Furthermore, we verify universal low-temperature power laws in the cooling rate and entropy, in particular linear scaling of entropy with temperature T in the gapless Luttinger-liquid state and scaling as √ T at field-induced transitions to gapped phases.

The Ising chain consisting of the antiferromagneticaly coupled ferromagnetic trimer is considered in the external magnetic field. In the framework of the transfer-matrix formalism the thermodynamics of the system is described. The magnetization per site (m) is obtained as the explicit function of the external magnetic field (H). The corresponding plots of m(H) are drawn. Two qualitatively different regions of the values of coupling constants are established: weak antiferromagnetic coupling (J A < 3J F ) and the strong antiferromagnetic coupling (J A ≥ 3J F ). For the latter case the magnetization curve with plateau at m/m sat = 1/3 is obtained. It is proven that the plateau is caused by the stability of spatially modulated spin structure 3111 . The values of magnetic field determining the width of the plateau are obtained in the limit of zero temperature. * E-mail address: vohanyan@www.physdep.r.am Fig. 4 The magnetization curves for κ = 6 at different temperatures: (a) T = 2.5J F ; (b) T = 0.8J F ; (c) T = 0.1J F ; (d) T = 0.001J F .

We consider the exactly solvable spin-1/2 XX chain with the three-spin interactions of the XZX + Y ZY and XZY − Y ZX types in an external (transverse) magnetic field. We calculate the entropy and examine the magnetocaloric effect for the quantum spin system. We discuss a relation between the cooling/heating efficiency and the ground-state phase diagram of the quantum spin model. We also compare ability to cool/heat in the vicinity of the quantum critical and triple points. Moreover, we examine the magnetocaloric effect for the spin-1/2 XX chain with three-spin interactions in a random (Lorentzian) transverse magnetic field.

We study a spin-1/2 model with triangular XXZ clusters on the orthogonal-dimer chain in the presence of an external magnetic field. First, we discuss the case where the triangular clusters are coupled via intermediate "classical" Ising spins. Diagonalization of the triangular XXZ clusters yields the exact ground states; finitetemperature properties are computed exactly by an additional transfer-matrix step. A detailed analysis reveals a large variety of ground states at magnetization M equal to fractions 0, 1/4, and 1/2 of the saturation magnetization M = 1. Some of these ground states break translational symmetry spontaneously and give rise to doubling of the unit cell. In a second part, we present complementary numerical data for the spin-1/2 Heisenberg model on the orthogonal-dimer chain. We analyze several examples of T = 0 magnetization curves, entropy as a function of temperature T and magnetic field, and the associated magnetic cooling rate. Comparison of the two models shows that in certain situations the simplified exactly solvable model yields a qualitatively or sometimes even quantitatively accurate description of the more challenging quantum model, including a case which may be relevant to experimental observations of an enhanced magnetocaloric effect in the two-dimensional compound SrCu 2 (BO 3 ) 2 .