Phase diagram of the triangular-lattice Potts antiferromagnet

50 pags., 19 figs., 5,2 tabs., app.We study the phase diagram of the triangular-lattice Q-state Potts model in the real -plane, where 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 RSOS model on the torus, for integer . 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.We thank Alan Sokal for the kind permission to use computational resources (provided by Dell Corporation) at New York University. JS is grateful for the hospitality from 2009 to 2017 of the Laboratoire de Physique Théorique at the École Normale Supérieure where part of this work was done. The research of JLJ was supported in part by the Agence Nationale de la Recherche (grant ANR-10-BLAN-0414: DIME), the Institut Universitaire de France, and the European Research Council (through the advanced grant NuQFT). The research of JLJ and JS was supported in part by Spanish MINECO grant FIS2014-57387-C3-3-P. The work of CRS was performed under the auspices of the U.S. Department of Energy at the Lawrence Livermore National Laboratory under Contract No DE-AC52-07NA27344.Peer Reviewe