Surface phase transitions of the three-dimensional semi-infinite spin-32Blume-Emery-Griffiths model

Abstract

Surface critical behaviors of a three-dimensional semi-infinite spin-$\frac{3}{2}$ Blume-Emery-Griffiths model are investigated in the framework of the mean-field approximation, devoting particular attention to repulsive biquadratic couplings. Self-consistent equations for bulk and surface order parameters are calculated, from which analytical expressions for the second-order bulk and surface critical temperatures are derived. Various qualitative types of phase diagrams, characterizing phase transitions of the model, are determined and classified according to the values of the interactions on the surface and in the bulk of the system. Our analysis shows the existense of a large number of topologies revealing the occurrence of surface and extraordinary first-order transitions and reentrant phenomenon. Successive phase transitions involving all phases, among which high-entropy ferrimagnetic and staggered quadrupolar orderings, and critical, tricritical, triple, multicritical, tetracritical, and five-phase coexistence points are also obtained.