Melting in two dimensions: first-order versus continuous transition

In the framework of the theory, based on the density functional theory of freezing, the melting of the system with Yukawa potential and the hard-disk system with square-well attraction is considered. It is shown that melting scenario crucially depends on the shape of the potential. For the soft-core Yukawa potential melting mainly occurs by means of two continuous transitions, however, there is the critical value of the radius of the potential where the crossover from two continuous to one first-order transition occurs. It should be noted that the first-order transition exists only for very short-range interaction. In the case of hard-core square-well potential situation is more complex, and there are several crossover points, where the melting scenario changes from continuous to first-order transition, and vice versa.