Theoretical Investigation On Phase Transition Of Transverse Spin-2 Ising Model With Different Single-ion Anisotropies

Ising model is a representative model for the studies of phase transition. Great emphasis has been given to the solution of extended Ising model and its application. Ising model is of great academic value for studying the properties of magnetic material in both fundamental magnetic physics and material science. Recently, there are lots of studies dealing with extended Blume-Capel model (only linear exchange interaction and crystal field are concerned) and extended Blume-Capel model (transverse BC model and diluted BC model). However, the results of the previous works about the first-order phase transition are confused and even contradict each other.In this paper, the properties of the phase transition in the transverse spin-2 Ising model with different single-ion anisotropies (crystal field) are studied employing mean-field theory and correlated effective-field theory. The effects of crystal field and transverse field on the first-order and second-order phase transitions are clarified.The main results are as follows.1. The transverse spin-2 Ising ferromagnetic model with longitudinal crystal field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The expressions of magnetization and free energy in the ground state and at finite temperature state are obtained by diagonalizing the Hamiltonian H_i of the system numerically. The phase diagrams are given, too. The great emphasis has given to the effect of crystal field and transverse field on the phase diagrams, magnetization curves and free energy curves of the spin system. The properties of the phase transition in the system are analyzed systemically; especially the first order-order phase transitions are studied in details for the first time. The results show that the first order-order phase transitions only appear in the very narrow range of crystal field and transverse field; the first order-disorder phase transitions appear in the wider range; and the second order phase transitions appear in the widest range except for the forenamed. Transverse field reduce crystal field range of the first order phase transition in BC model till crystal field range disappears, namely transverse field can weaken the first order phase transition trend of the system. The re-entrant phenomenon occurs when the value of transverse field is not zero at finite temperature. In addition hysteresis phenomenon is found in the...