The first- and second-order phase transitions of the q-state Potts models are obtained in arbitrary dimension d. Critical and tricritical behaviours merge and annihilate at q c (d), clearing the way to first-order transitions at q>q c (d) by the condensation of effective vacancies. The value of q c (d) decreases with increasing d, from diverging as exp(2/(d-1)) at d to 1 + , to q c (2)=3.81 (cf exact value of 4), to lower values at d>2. For given d, a changeover in critical behaviour occurs at q 1 (d), as the critical fixed points merge from the Potts-lattice-gas region to the undiluted Potts limit. It is suggested that the power law singularities of the percolation problem (q to 1 + ) have logarithmic corrections.
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Andelman et al. (1981) studied this question.