Correlated Effected-field Investigation On Spin-2Ising Model In Transvese Field

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-2Ising model with crystal field are studied employing correlated effective-field theory. The effects of crystal field and transverse field for honeycomb lattice, square lattice and simple cubic lattice on the first-order and second-order phase transitions are clarified.The main results are as follows.1. Ground-state properties of honeycomb lattice, square lattice and simple cubic lattice are studied in correlated-field theory and the internal energy is used as a criterion for first-order phase transition. First order and second order phase transition are found in three kinds of lattices and the tricritical point does exist. The second order phase transition will appear first in three cases. But the order for the apperence of the first order-disorder phase transition in these three lattices is different. The first order-order phase transition will appear first in honeycomb lattice and the first order-disorder phase transition will appear first in the other two kinds of lattices. Ground-state phase diagrams for three kinds of lattices are given in this paper. We find that the absolute value of crystal field for honeycomb lattice’s tricritical point is the biggest one. But the tricritical points for the other two kinds nearly equal to each other. Free energy will decrease with the change of crystal field and transverse field in our given free energy diagrams.2. Magnetization, internal energy, specific heat and free energy for honeycomb lattice are studied at finite temperature and three kinds of magnetizations are given. There is another interesting second order-order phase transition except first order, second order phase transition and reentrantant phenomenon. The greater the transverse field, the less region it appears. So the transverse field will suppress its occurrence. There is a jump in the internal energy curve for first order phase transition and an inflection point for second order phase transition. Internal energy will decrease when the system’s high symmetry state changes to the low symmetry state. It means that symmetry can affect system’s internal energy. Specific heat of second order phase transition is a limited peak; otherwise there is an infinite point for the first order phase transition. That is because the process of first order phase transition accompanies with the latent heat. Second order phase transition has little effect on free energy and its free energy is a continuous data points. First order phase transition is an inflection point in the free energy curve.3. The properties of square lattice and simple cubic lattice are studied as well and their magnetization, phase diagram and free energy are given.They also have the same phase transition contrasted to honeycomb lattice. The order of phase transition appearing is the same for three kinds of lattices in our given phase diagrams. The second phase transition always occurs first, while the first order phase transition will appear when the absolute of crystal field takes a big value. Only second phase transition exists in a high transverse field. The larger the transverse field, the less the absolute value of reentrantant phenomenon’s crystal field. This indicates that crystal field will promote the first order phase transition and transverse field will inhibited the first order phase transition.The second order phase transition will always exist no matter what value transverse field takes. That means transverse field play a positive role for the second order phase transition. There is an inflection point of first order phase transition in our given free energy curves. But there are not any manifest features about the second order phase transition and reentrantant phenomenon. The absolute value of the crystal field together with the transition temperature for the simple cubic lattice is larger than the one of square lattice when the phase transition occures. The free energy of simple cubic lattice is higher than the one of square lattice when crystal and transverse field take the same value.