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Phase diagram of the triangular-lattice Potts antiferromagnet. (English) Zbl 1376.82018

Summary: We study the phase diagram of the triangular-lattice \(Q\)-state Potts model in the real \((Q, v)\) -plane, where \(v={\mathrm e}^J-1\) 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 \(p=4, 5, \dots, 8\). 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.

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
82D40 Statistical mechanics of magnetic materials
82B27 Critical phenomena in equilibrium statistical mechanics
82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics

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