Monte Carlo study of the triangular XY vector Blume-Emery-Griffiths model

The vectorial generalization of the Blume-Emery-Griffiths model, proposed by Berker and Nelson to describe the behavior of films of 3He-4He mixtures, is studied by Monte Carlo simulations on the triangular lattice. The temperature versus chemical potential plane phase diagram, for a biquadratic coupling constant equal to the bilinear coupling constant, presents a Berezinzkii-Kosterlitz-Thouless transition line that ends in a first-order transition line at a critical end point. This first-order transition line, on the other hand, terminates at a single critical point. No tricritical point has been detected. The critical exponent η as a function of temperature is independent of the chemical potential.