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Phase diagrams in the Blume-Emery-Griffiths Ising films

We study the spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field. In addition to the four usual phases: disordered DIS, ferromagnetic FER, antiquadrupolar AQU and ferrimagnetic FRI, we found three new phases in the case of a thin magnetic film, namely: the sublattice A non magnetic phase NMA, the sublattice B non magnetic phase NMB and the global non magnetic phase NMG. These phases are studied, for each layer of the film, either in the temperature-crystal field plane $(T,Δ)$ or in the biquadratic coupling-crystal field plane $(d,Δ)$, for diferent film thicknesses. On the other hand, the thermal behaviour of the layer quadrupolar moments $q_{A}, q_{B}$ and layer magnetisations $m_{A}, m_{B}$ are investigated for negative values of the biquadratic coupling and crystal field. It is also found that for fixed values of the biquadratic coupling, the temperature and the crystal field, each layer of the film can belong to a differnt phase. To illustrate this situation, an example is given for $d=-3.0$, $Δ=-3.0$ and $T=1.3$.