Abstract
Abstract A quantum Ising-like spin-1 system with both dipole and quadrupole interactions is analyzed. Such model is a generalized quantum version of the Blume-Emery-Griffiths model in an external anisotropic field. Models of this type are interesting candidates to describe phase transitions in liquid crystals. The phase diagram as well as the thermodynamic potentials of the model are constructed by a recently formulated improved version of mean field theory. The latter, which has the usual mean field theory as its zero-th order approximation, takes into account fluctuations up to the fourth-order. The phase diagram is found to exhibit phase transition manifolds of both the first and the second order, as well as multicritical lines. Four phases can be recognized: one ferromagnetic and three paramagnetic. The phases are identified by the requirements of minimum free energy constrained by the condition of self consistency of the order parameters p and q
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