Phase transition in the high-order nonideal mixing model

We extend the existing second-order nonideal mixing model, which only formally allows for the second-order phase transition, into the fourth-order. The Landau theory reveals that both first- and second-order phase transitions may exist in this higher-order model. Moreover, we show that a single structural parameter determines whether the phase transition abruptly switches between first- and second- orders. We note, it provides an explanation of either appearance or absence of the liquid-liquid critical point in the liquid-liquid phase transition on debate.