Phase diagram and tricritical behavior of the spin-1 Heisenberg model with Dzyaloshinskii–Moriya interactions

Thermodynamic properties and phase diagrams of spin-1 quantum Ising systems with three-spin interactions

“…On the other hand, the stable magnetization drops discontinuously from a finite value m * F (D 0 ) to zero at a temperature T F (D 0 ), which characterizes a first-order phase transition. The first-order phase transition temperature T F (D 0 ) can be obtained by the free energy, when its local minimum at m = 0 is equal to the local minimum at m = 0 [36,37]. When the reduced crystal-field parameter is slightly larger than the tricritical point D tr 0 (1.95138), the system can undergo the first-order phase transition, such as, for D 0 = 1.98 the first-order The Hamiltonian of the spin-1 quantum Ising system with biquadratic interactions on a triangular lattice is defined as…”

“…In the following discussion, the coupling constant J > 0, that is, a ferromagnetic case is considered. Based on the mean-field approximation [36,37], the three-spin cluster Hamiltonian H 123 can be written as…”