The Effects of the Random Transverse Crystal Field on the Spin-1 Model

The effects of random transverse crystal field are investigated in the mean-field approximation on the spin-1 model. The transverse crystal field is applied on a lattice in a bimodal random distribution with a tunable parameter adjusting the strength of one mode with respect to the other one. Then, the phase diagrams are calculated on the reduced temperature-transverse crystal field planes for given values of probability p and coordination number q at zero external magnetic field h. It was found that the model gives both second- and first-order phase transitions and tricritical points which is a well-known behavior of the spin-1 model. In addition, the model also yields critical end points and end points for the first-order phase transition lines for appropriate p values.