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Tricriticality of the Blume-Emery-Griffiths Model In Thin Films of Stacked Triangular Lattices

We study in this paper the Blume-Emery-Griffiths model in a thin film of stacked triangular lattices.The model is described by three parameters: bilinear exchange interaction between spins $J$, quadratic exchange interaction $K$ and single-ion anisotropy $D$. The spin $S\_i$ at the lattice site $i$ takes three values $(-1,0,+1)$.This model can describe the mixing phase of He-4 ($S\_i =+1,-1$) and He-3 ($S\_i =0$) at low temperatures.Using Monte Carlo simulations, we show that there exists a critical value of $D$ below (above) which the transition is of second-(first-)order.In general, the temperature dependence of the concentrations of He-3 is different from layer by layer. At a finite temperature in the superfluid phase, the film surface shows a deficit of He-4 with respect to interior layers. However, effects of surface interaction parameters can reverse this situation. Effects of the film thickness on physical properties will be also shown as functions of temperature.