Renormalization-group theory of an internal critical-end-point structure: The Blume-Emery-Griffiths model with biquadratic repulsion

A prefaced renormalization-group study indicates that all three features of the Blume-Emery-Griffiths model with repulsive biquadratic interaction, namely (1) a critical-end-point structure occurring inside the ferromagnetic phase, (2) disordered-ferromagnetic-disordered reentrance, and (3) a ferrimagnetic phase sandwiched between the ferromagnetic and antiquadrupolar phases, survive fluctuations in three dimensions but not in two dimensions. The renormalization-group mechanism for a critical-end-point structure inside the ordered phase is shown to be the same as that originally found for a critical-end-point structure inside the disordered phase, namely a distinct hybrid fixed point, contrary to a previous claim.