The Study Of Magnetization And Phase Transition Of Blume-Capel On Nanotube

Recently, the Blume-Capel model has received a great deal of attention. Using the effective field theory, the magnetization and phase transition of spin-1Blume-Capel model with random crystal field on a cylindrical nanotube are studied.The main results are given as follows:For the Blume-Capel model, the effects of the ratios of crystal field and the crystal field interaction on magnetization of system are investigated on a cylindrical nanotube. It is shown that the negative crystal field weakens the magnetization. The temperature dependence of the magnetization shows that the system presents the first-order phase transition when the negative crystal field is stronger and the probability of random crystal fields takes constant. The system exhibits two critical temperatures which are a temperature of paramagnetic phase transition and a temperature of ferromagnetic phase transition when the probability of random crystal fields and negative crystal field take constant. For 0 ?p ?1 and the negative crystal field is stronger, the values of magnetization are 1TM ? at the ground state. The magnetization is also studied when the temperature keeps constant. The magnetization of the surface shell1 m,2m and the core shellcm are investigated. When the probability of random crystal fields takes constant and the values of negative crystal field are smaller, the values of magnetization are1 21 cm ?m ?m ? at the ground state; however,the negative crystal field is stronger, the values of magnetization are1 21 cm ?m ?m ?.For the Blume-Capel model, the effects of the ratios of crystal field and the crystal field interaction the phase transition of system are investigated on nanotube.The ratios of crystal field dependence of phase transition temperature shows that the phase transition temperature reduces gradually with the increasing of ratios of crystal field under the action of negative crystal field. The smaller of probability of random crystal fields is, the higher the phase transition temperature is when the ratio of crystal field takes a certain constant. However, the larger of probability is, the higher the phase transition temperature is when the ratio of crystal field takes a certain constant under the action of positive crystal field. We observe the phase transition when the ratio of crystal field takes different values. The system exhibits the tricritical points and reentrant phenomenon for an appropriate range of probability of random crystalfields. In addition, the tricritical points disappear for changing the range of probability.The curves of second-order phase transition show that critical temperature approaches finite value as D J ? ??. These results attributed to competition the exchange interaction, crystal field, the ratios of crystal field and the probability of random crystal fields.