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 [Formula: see text], quadratic exchange interaction [Formula: see text] and single-ion anisotropy [Formula: see text]. The spin [Formula: see text] at the lattice site [Formula: see text] takes three values [Formula: see text]. This model can describe the mixing phase of He-4 [Formula: see text] and He-3 [Formula: see text] at low temperatures. Using Monte Carlo simulations, we show that there exists a critical value of [Formula: see text] 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.