横场和晶场作用下S=2的Ising模型的磁性质

The Magnetic Properties of the Spin-2 Ising Model Under the Transverse Field and Crystal Field

采用平均场理论,计算了高自旋S=2且处于外界横向磁场的Ising模型,推导出系统有限温度下磁矩及自由能的理论计算公式,利用数值计算方法得到了系统在有限温度下的磁化曲线,重点考察了有限温度下纵向晶场D和横场Ω对自旋系统磁化曲线及自由能的影响。从磁化曲线中观察到了4种相变特征:一级有序-有序相变、一级有序-无序相变、二级有序-无序相变及重入现象。研究发现重入现象只发生于存在横向磁场的情况下;一级相变发生在狭小的晶场和横场范围内,一级有序-有序相变的存在范围更加狭小,而二级有序-无序相变存在于较大的晶场和横场范围内;总体上说一级相变对应的温度较二级相变对应的温度低;晶场是促进相变发生的因素;横场是限制相变发生的因素。

The mean-field theory was adopted to calculate the high spin-2 transverse Ising model. Theoretical expressions for magnetic moment and free energy were deduced at finite temperature. Magnetization curves of the system at the limited temperature were obtained by the use of numerical calculation. The study emphases on examining the influence of crystal field D and transverse field Ω on magnetization curves of spin systems and free energy. Characteristics of four phase transitions were observed in the magnetization curves： first order-order phase transition, first order-disorder phase transition, second order -disorder phase transition and reentrant phenomenon. The results show that reentrant phenomenon appears only when transverse field is not equal to zero; first - order phase transition appears in the very narrow range of crystal field and transverse field; the scope of first order-order phase transition is narrower; second order - disorder phase transition occurs in the wide range of crystal field and transverse field. In general the temperature of the first - order phase transition is lower than that of the second - order phase transition. Crystal field is a factor to accelerate phase transitions, and transverse field is a factor to limit phase transitions.