Phase diagram of the Blume-Emery-Griffiths model on the simple cubic lattice calculated by the linear chain approximation

The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupol e coupling strengths and a crystal-field interaction. The problem is approa ched introducing first a trial one-dimensional Hamiltonian whose free energ y can be calculated exactly by the transfer matrix method. Then using the B ogoliubov variational principle, the free energy of the model is determined . It is assumed that the dipolar and quadrupolar intrachain coupling consta nts are much stronger than the corresponding interchain constants and confi ned the attention to the case of nearest-neighbor interactions. The phase t ransitions are examined and the phase diagrams are obtained for several val ues of the coupling strengths in the three different planes. A comparison w ith other approximate techniques is also made. (C) 2000 Elsevier Science B. V. All rights reserved.