A cluster variation approach to the random-anisotropy Blume-Emery-Griffiths model

Abstract

The random-anisotropy Blume-Emery-Griffiths model, which has been proposed to describe the critical behavior of 3 He-4 He mixtures in a porous medium, is studied in the pair approximation of the cluster variation method extended to disordered systems. Several new features, with respect to mean field theory, are found, including a rich ground state, a nonzero percolation threshold, a reentrant coexistence curve and a miscibility gap on the high 3 He concentration side down to zero temperature. Furthermore, nearest neighbor correlations are introduced in the random distribution of the anisotropy, which are shown to be responsible for the raising of the critical temperature with respect to the pure and uncorrelated random cases and contribute to the detachment of the coexistence curve from the λ line.

Real-space renormalization-group study of the two-dimensional Blume-Capel model with a random crystal field

“…Its Hamiltonian reads: H = H BC − K <i,j> S 2 i S 2 j and the parameters J, K and ∆ were originally related to the energy interactions between the constituents of the system. In 3 He- 4 He mixtures, the state S = 0 represents a 3 He atom while 4 He atoms are denoted by S = ±1 states: the superfluid transition corresponds to the symetry breaking between the ±1 states.…”

The Effect of a Random Crystal-Field on the Mixed Ising Spins (1/2, 3/2)

“…In this model, a negative crystal-field value represents the field at the pore-grain interface and a positive value is a bulk field that controls the concentration of 3 He atoms [26][27][28].…”

Effects of the Quenched Random Crystal Field on the Dynamic Spin-1 Blume-Capel Model

“…This model is used to describe the phase separations of superfluidity for helium mixtures in aerogel [26,27]. Due to this fact, various researchers have been motivated to study the effect of the crystal field disorder on the multicritical phase diagram of BC model via effective field theory [28], mean field approximation [29][30][31][32][33], cluster variation method [34], as well as by introducing an external random field [35]. Branco et al considered the effects of random crystal fields using real-space RG [12,13] and mean-field approximations [13,36] for BC and BEG model Hamiltonians.…”