The Phase Transition Properties Of Random Transverse Uniaxial And Biaxial Crystal Field Blume-emery-griffiths Model

Within the framework of the effective field theory (EFT) and cutting approximation,the phase transition properties of spin-1random transverse uniaxial and biaxial crystal fieldBlume-Emery-Griffiths (BEG) model are investigated. Some new phenomena arepresented.Firstly, we study the phase diagrams of random transverse crystal field BEGM. Thephase diagrams are given inT D_xand T αspace. When0> α>1, it represents aweak repulsive potential. The tricritical point (TCP) appears, which undergoes a crossoverfrom positive to negative direction of transverse crystal field for a tunable parameter l <0.When α>0, it means an attractive potential. The TCP is not observed and the range ofordered phase is magnified. When α≤1, it represents a strong repulsive potential, thephase lines between the staggered quadrupolar phase and paramagnetic phase (SQ-P)extend to D_x/Jâ†'±∞or converge to some D_x/Jvalues when the random transversecrystal field has two parts with different values in the same or opposite direction. There is afixed degenerate state of transverse crystal field for l=±0.5at D_x/J=0and anambulatory degenerate state for l=0.5at D_x/J>0.Secondly, the phase transition properties of biaxial BEG model with both longitudinaland transverse crystal field are investigated on simple cubic lattice. Here, the transversecrystal field is dilution distribution. InT D_zspace, when α represents a weakrepulsive potential, the reentrant phenomenon first enhances, and then weakens when thevalue of D_x/Jis changed from+3.0to7.0. When introducing dilution oftransverse crystal field, both the reentrant phenomenon and TCP show a richdiversification. When α turns into a weak attractive potential, the range of the orderedphase magnifies. Two TCPs exists in the phase transition line, which performs as afirst-order transition line between two second-order transition lines, defined as A-type double TCPs. InT D_xspace, one degenerate state appears in the pure situation whenα <0. The introduction of dilution can destroy the degenerate state. Meanwhile, anotherB-type double TCPs phenomenon occurs in the phase transition line, which can beexpressed as a second-order transition line between two first-order transition lines. Twodegenerate states appear in the pure situation when α>0, the introduction of the dilutiondoesn’t completely destroy the degenerate pattern, but the degree of degenerate dropsclearly. Particularly, a novel three TCPs appear in the transition line when D_z/J=4.5.The three TCPs come from the conformation both A-type and B-type double TCPs. Whenα is chosen as a strong repulsive potential, the phase separation and TCP coexist inT αspace，which can be depressed by the dilution of the transverse crystal field.Without longitudinal crystal field inT D_xspace, the SQ-P phase lines extend toD_x/Jâ†'+∞. With the increase of the repulsive potential, the range of ferromagneticphase decreases, while the staggered quadrupolar phase enlarges. InT D_zspace, whenthe transverse field changes from positive to negative in the pure state, the range of SQphase first reduces and then expands, meanwhile, the double critical point (BCP) firstdecreases and then increases. The dilution can create an abnormal critical behavior whenthe value of negative transverse crystal field is large.