A New Disordered Phase and Its Physical Contents of the Blume-emery-griffiths Model

Thermodynamic properties of the anisotropic BlurneEmery-Griffiths model are discussed in the new type of effective-field theory, A new disordered phase which may correspond to the staggered quadrupolar phase predicted by the Monte Carlo simulation is found and its physical contents are investigated. The anisotropic Blume-Emery-Griffiths (BEG) a where V, = ( p = X, y) gives the two differential model is a sain-one Isine: model with bilinear and biau quadratic nkest-neighbor pair interactions in which operators, and'the functions f~ (X, Y) and g~ (X, Y) a single-ion anisotropy parameter is included [l]. The are defined by BEG model has been investigated theoretically by many authors in connection with the experimental 2eY sinh (X + h) results on magnetic phase transitions in some comfH ' 1 = 2ey cosh (X + h) + exp (-BD) (4) pounds and phase separation of a binary fluid. The Hamiltonian of the model is given by where Jij, J:~ and D are the bilinear, biquadratic and anisotropy parameters, respectively. H is the applied magnetic field. Each S: can take the values f l and 0, and the summation is carried out over all pairs of nearest-neaghbor spins. Recently, the existence of a new disordered phase, namely the staggered quadrupolar phase, has been predicted from the Monte Carlo simulation, for when the conditions of J + J' < 0 and D > 0 are satisfied in the BEG model [2]. In the preceding studies [3, 41 we have found a new disordered phase which may correspond to the staggered quadrupolar phase by the use of the effective-field theory with correlations (EFT). The purpose of this work is to clarify the physical contents of the new disordered phase in the BEG model. Following the formulation by Fittipaldi and Siqueira (F-S) [5] for the BEG model, the statistical mechanical quantities m = (S;) and q = ((s;)~) for a honeycomb lattice may be evaluated from the following set of equations, within the framework of the EFT, m = [l + m sinh (kV,) + Q {cosh (KVx) Ill3 X 2eY cosh (X + h) gx= (X, Y) = 2eY cosh (X + h) + exp (-BD) (5) with p = l/kBT and h = OH, where K and K' are defined by K = ,B J and K' = ,l3 J'. On the other hand, the initial susceptibility per site is defined by which is given by a complex equation, after deferentiating (2) with H and substituting ?!into it. aH However, the paramagnetic susceptibility has a simple form, which is given by