Phase diagrams of the Blume-Emery-Griffiths model: real-space renormalization group investigation and finite size scaling analysis

An approximate real-space renormalization group scheme based on the Migdal-Kadanoff recursion relations and the finite size scaling method are used to study the phase diagrams of the two-dimensional spin-1 Ising model with nearest-neighbor interactions, both bilinear and biquadratic, and with a crystal-field interaction. Contrary to previous studies, we clarify the behavior of the model at low temperature including the region J + K < 0 and Δ<0, where a staggered quadrupolar phase appears. With both methods we show that the staggered quadrupolar and the ferromagnetic phases are separated by a disordered phase, and the second-order phase boundary lines of the two ordered phases meet only at zero temperature.