Phase diagrams of the three-dimensional semi-infinite Blume-Emery-Griffiths model

Within a real-space renormalization-group framework based on the Migdal-Kadanoff recursion relations, we investigate the three-dimensional semi-infinite Blume-Emery-Griffiths model with nearest-neighbor interactions, both bilinear and biquadratic, and with a crystal-field interaction. According to the values of the interactions on the surface and in the bulk of the system, we determine the various generic types of phase diagrams in the case of repulsive biquadratic interactions. Our analysis has led to a classification scheme with eleven fundamental types of phase diagrams describing a large variety of phase transitions associated with the surface and multicritical topologies.