Multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution

Abstract

As a continuation of the previously published work, the pair approximation of the cluster variation method is applied to study the temperature dependences of the order parameters of the Blume–Emery–Griffiths model with repulsive biquadratic coupling on a body centered cubic lattice. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. We study the dynamics of the model by the path probability method with pair distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagram in addition to the equilibrium phase diagram and also the first-order phase transition line for the unstable branches of the quadrupole order parameter is superimposed on the phase diagrams. It is found that the metastable phase diagram and the first-order phase boundary for the unstable quadrupole order parameter always exist at the low temperatures which are consistent with experimental and theoretical works.