A TEM and XRD study of the SbNbSe3 misfit layer structures

Two new misfit layer structures have been synthesized within the Sb-Nb-Se system. Powder X-ray diffraction and electron microscopy techniques (electron diffraction, HREM, XEDS) have been used to determine the nature of their structure. According to TEM and XEDS data (for more than 15 crystals studied) both phases are monolayer type, i.e. (SbSe)1+delta (NbSe2). Electron microscopy reveals a composite modulated structure that consists of the periodical intergrowth of a pseudotetragonal SbSe layer, denominated as Q, and a pseudohexagonal layer NbSe2, denominated as H. Both layers fit along b, stack along c and do not fit along a (misfit) giving rise to an incommensurate modulation along this direction. The two phases differ in the symmetry of the Q layers being in one case orthorhombic (for delta = 0.17) and monoclinic in the other (for delta = 0.19). After the characterization of the sample by electron microscopy the unit cells of the basic layers could be refined for both phases by powder X-ray diffraction: aQ = 5.824(2) A, bQ = 5.962(5) A, cQ = 23.927(6) A, alpha = 90 degrees, beta = 90 degrees and gamma = 90 degrees and aH = 3.415(5) A, bH = 5.962(6) A,, cH = 11.962(1) A, alpha = 90 degrees, beta = 90 degrees and gamma = 90 degrees for the orthorhombic phase; aQ = 5.844(2) A, bQ = 5.981(1) A, cQ = 23.919(5) A, alpha = 90 degrees, beta = 90 degrees and gamma = 96.00(3)degrees and aH = 3.439(1) A, bH = 5.994(2) A, cH = 11.956(3) A, alpha = 90 degrees, beta = 90 degrees and gamma = 90 degrees for the monoclinic phase. The phase with the monoclinic Q-sublattice often appears as twinned crystals. The more abundant crystals are disordered intergrowths of both monolayer phases.     

Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain

The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.     

Infinite-dimensional gauge Ising model

Erevan Physics Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 2, pp. 281–288, February, 1989.     

An exact solution on the ferromagnetic face-cubic spin model on a Bethe lattice

The lattice spin model with Q-component discrete spin variables restricted to have orientations orthogonal to the faces of Q  -dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole–dipole and quadrupole–quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations (RR) which allows to calculate all thermodynamic characteristics of the model is obtained. The correspondence between thermodynamic phases and different types of fixed points of the RR is established. Using the technique of simple iterations the plots of the zero field magnetization and quadrupolar moment are obtained. Analyzing the regions of stability of different types of fixed points of the system of recurrent relations the phase diagrams of the model are plotted. For Q?2$Q?2$ the phase diagram of the model is found to have three tricritical points, whereas for Q>2$Q>2$ there are one triple and one tricritical points.     

Cyclic period-3 window in antiferromagnetic potts and Ising models on recursive lattices

The magnetic properties of the antiferromagnetic Potts model with two-site interaction and the antiferromagnetic Ising model with three-site interaction on recursive lattices have been studied. A cyclic period-3 window has been revealed by the recurrence relation method in the antiferromagnetic Q-state Potts model on the Bethe lattice (at Q < 2) and in the antiferromagnetic Ising model with three-site interaction on the Husimi cactus. The Lyapunov exponents have been calculated, modulated phases and a chaotic regime in the cyclic period-3 window have been found for one-dimensional rational mappings determined the properties of these systems.     

Magnetic properties and quantum entanglement on decorated zigzag ladder

Magnetic properties and quantum entanglement of Heisenberg model with two-, three- and four-site exchange interactions on zigzag ladder are studied. Magnetic properties and concurrence (measure of quantum entanglement) are analyzed by means of variational mean-field-like treatment based on the Gibbs-Bogoliubov inequality. The magnetization plateau and second-order phase transition are obtained. A comparison of the entanglement and magnetic characteristics for the zigzag ladder is made. Our calculations show that in the antiferromagnetic region the behavior of the concurrence coincides with that of the magnetization.     

Topological aspects of gauge and spin potts models

For the d-dimensional lattice gauge Potts model the representation of the partition function is derived, where the field configuration summation is reduced to the summation over submanifolds (oriented and nonoriented), constructed from the plaquettes of the lattice. The topological invariants (Betti numbers) of these two-dimensional submanifolds are used in an essential way. Some possible applications of this representation for the partition function are discussed.     

Magnetization and Lyapunov exponents on a kagome chain with multi-site exchange interaction

The Ising approximation of the Heisenberg model in a strong magnetic field, with two, three and six spin exchange interactions is studied on a kagome chain. The kagome chain can be considered as an approximation of the third layer of ³He absorbed on the surface of graphite (kagome lattice). By using dynamical approach we have found one- and multi-dimensional mappings (recursion relations) for the partition function. The magnetization diagrams are plotted and they show that the kagome chain is separating into four sublattices with different magnetizations. Magnetization curves of two sublattices exhibit plateaus at zero and 2/3 of the saturation field. The maximal Lyapunov exponent for multi-dimensional mapping is considered and it is shown that near the magnetization plateaus the maximal Lyapunov exponent also exhibits plateaus.