Study On The Critical Properties Of The Random Two-dimensional Ferromagnetic System

The ferromagnet shows strong magnetism in the condition of low temperature. But when the temperature reaches the Curie temperature the ferromagnet turns into paramagnet. It is the second-order phase transition from ferromagnet to paramagnet. With the effect of inner field and outer field, Curie temperature will decrease and the system will shows many kinds of properties of phase transition.This article mainly discusses the critical properties of single spin (S=l) ferromagnetic system. In this article we introduce the bond-dilutied Blume-Capel model (BCM) with the random crystal field and combine the BCM as well as the transverse Ising model (TIM) with the random crystal field. The phase diagrams display the Curie temperature dependences of the crystal field, the transverse field, the bond concentration and the random crystal field concentration for the honeycomb lattice and the square lattice. In the BCM with random crystal field, the Curie temperature decreases monotonously with the increasing of the crystal field. The system with a larger crystal field can exhibit tricritical point at which the phase transitionchanges from second to first order. When the random concentration of the crystal field decreases the tricritical point is depressed, at the same time the reentrant phenomenon occurs. The system will be ordered entirely when the random concentration is small enough at low temperatures. Due to the difference of coordination number, the honeycomb lattice and the square lattice display different transition properties. The bond dilution can depress the order phase effectively. When transverse field is introduced we adopt bond-diluted the MCM+TIM with random crystal field. The transverse field can also decrease the critical temperature. At the same time it can depress the tricritical point and the reentrant phenomenon. The competition between these factors shows some new critical features. We obtain a series of meaning results.