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.