Spontaneous magnetization of the Blume-Emery-Griffiths model at the ferromagnetic-antiquadrupolar-disordered interface

In this paper we study the spontaneous magnetization of the Blume-Emery-Griffiths (BEG) model at the ferromagnetic-antiquadrupolar-disordered (FAD) interface. We introduce a Gibbs sampler of the ground states at zero temperature, and we exploit it in two different ways: first, we perform via perfect sampling an empirical evaluation of the spontaneous magnetization at zero temperature, finding a non-zero value in $D=3$ and a vanishing value in $D=2$. Second, using a careful coupling with the site percolation model in $D=2$, we prove rigorously that imposing $+$ boundary conditions in the BEG model at FAD interface the magnetization in the center of a square box tends to zero in the thermodynamical limit.