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

TL;DR

This study investigates the phase transitions of the Blume-Emery-Griffiths model in thin stacked triangular lattice films, revealing how parameters like anisotropy influence the order of phase transitions and layer-specific compositions.

Contribution

It provides the first Monte Carlo analysis of the model's tricritical behavior in thin films, highlighting the effects of surface interactions and film thickness on phase transition order.

Findings

Existence of a critical anisotropy value separating first- and second-order transitions.

Layer-dependent concentration differences of He-3 and He-4 at finite temperatures.

Surface effects can reverse the concentration deficit observed in interior layers.

Abstract

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.