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We study the phase diagram of the triangular-lattice Q-state Potts model in the real (Q, v)-plane, where v - e(J) - 1 is the temperature variable. Our first goal is to provide an obviously missing feature of this diagram: the position of the antiferromagnetic critical curve. This curve turns out to possess a bifurcation point with two branches emerging from it, entailing important consequences for the global phase diagram. We have obtained accurate numerical estimates for the position of this curve by combining the transfer-matrix approach for strip graphs with toroidal boundary conditions and the recent method of critical polynomials. The second goal of this work is to study the corresponding A(p-1) RSOS model on the torus, for integer p = 4, 5,..., 8. We clarify its relation to the corresponding Potts model, in particular concerning the role of boundary conditions. For certain values of p, we identify several new critical points and regimes for the RSOS model and we initiate the study of the flows between the corresponding field theories.
potts model; RSOS model; conformal field theory; transfer matrix; critical polynomial