MULTICRITICALITY IN A SELF-DUAL POTTS-MODEL

We explore the self-dual plane of a two-dimensional Potts model with vacancies and four-spin interactions, using finite-size scaling of transfer-matrix results. Since the transfer matrix construction is based on the random-cluster representation of the Potts model, its application is not restricted to an integer number q of Potts states. For q less-than-or-equal-to 4 the self-dual plane contains a critical region belonging to the ordinary Potts universality class, and a region of first-order transition points. The two regions am separated by a fine of which a range consists of Potts tricritical points, while another range is of a first-order nature. The point separating these two ranges is, for 0 < q less-than-or-equal-to 9/4, identified with the multicritical point of which an exact solution has recently been given by Nienhuis et al.