Title: Phase diagram of the triangular-lattice Potts antiferromagnet,
Abstract: 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 $p=4,5,\ldots,8$.
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.