The Study Of Phase Transitions Of Quantum Spin Systems With Dzyaloshinskii-Moriya Interactions

In this thesis, the phase transitions and thermodynamic properties of the quantum spin systems with Dzyaloshinskii-Moriya (DM) interactions are studied by means of the two-spin cluster mean-field method. The main results of this thesis are as follows:1. The critical properties of the spin-1 Heisenberg system with DM interactions on the simple cubic lattice are investigated. The phase diagram of the system and the thermal behavior of the magnetization in the Ising limit (A = l) are obtained. The results show that the system exhibits the tricritical point. It is found that the reduced tricritical temperature T-t is independent of the exchange anisptropy parameter A and is a certain value of T₁ =1.71, while the reduced tricritical DM parameter is given by2. The thermodynamic effects of DM interactions on the Blume-Capel (BC) systems on the honeycomb, square and simple cubic lattices are studied. The phase diagrams of the above systems for various values of the reduced DM interaction parameter D₀ are obtained. The results indicate that the three systems exhibit the tricritical point, and the tricritical temperature firstly decreases to a minimum and then increases with the increase of the DM interaction parameter.