Dublenych Y. Phase behaviour of some pseudospin and pseudospin-electronic models

The goal of the dissertation is to study phase transitions and phase separation in spin and pseudospin-electron models describing behavior of chains of apex oxygen ions in high-temperature superconductors of the YBa2Cu3O7-δ type, layered intercalated compounds, and some ferroelectrics. The pseudospin-electron model with a direct interaction between pseudospins and with a transverse field is considered in the mean-field approximation. In the absence of electron transfer, the equilibrium states of the model are studied in the mean field approximation. In the μ = const regime, two types of the first order phase transitions (with jumps of the mean values of pseudospins and average electron concentration) are revealed. At T → 0, phase transitions of the first type disappear, on increasing the transverse field, while those of the second type persist at any large value of the field. The phase transitions of the second type are caused by simultaneous effect of pseudospin-electron interaction and transverse field. It is also shown that in the n = const regime at zero temperature, the phase separation occurs at all values of a longitudinal field h. Within a simplified pseudospin model (without electrons and longitudinal field) the spectrum of CuO chains of finite length and intensities of transitions between levels are calculated. A transition occurs (from the ground state) in the low-energy part of the spectrum. The energy of this transition decreases with increasing number of fragments in the chain. Ground-state phase diagrams of the generalized Blume-Emery-Griffiths model on unfrustrated lattices, as well as on triangular and kagome lattices with the nearest neighbor interaction are constructed. It is shown that the ground state of a system of classical spins on a anisotropic triangular lattice with interactions within an elementary triangular plaquette can be constructed by minimizing the single plaquette energy density function. Even in the case when all the three angles between pairs of spins on the plaquette are different, there exist five types of global ground-state configurations. The most complicated of these is a spiral four sublattice ordering. On the base of this outcome the experimentally observed spin disorder in NiGa2S4 and FeGa2S4 compounds is explained. Some of the results of this study were used in another study where a pseudospin-electron model based on Blume-Emery-Griffiths model is considered and applied to describe the phase transitions and phase separations in intercalated crystals. It is shown that, due to the one-site character of the electron-electron and pseudospin-electron interactions, the partition function of such a model can be presented as the product of the partition functions of independent pseudospin with two shifted parameters and electron subsystems. The phase diagrams of the model as well as the phase separation diagrams and the dependencies of the concentration of intercalated particles on their chemical potential are constructed: exactly for zero temperature and in the mean field approximation for nonzero one. It is shown that in certain interval of chemical potential values the direct interaction between intercalated particles and basic layer electrons leads to the separation into phases with different particle and electron concentrations. Phase transitions in the Mitsui model without longitudinal field but with a transverse one are investigated in the mean field approximation. The one-to-one correspondence has been established between this model and the two-sublattice Ising-type model with longitudinal and transverse fields. Phase diagrams and diagrams of existence of the ferroelectric phase are constructed. In the case Ω = 0 (Ω is the transverse field), a simple analytical expression for the tricritical temperature and the condition of existence of the tricritical point are obtained. For Ω ≠ 0, systems of equations for the tricritical point and for the condition of its existence are determined.