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 $p=4,5,\dots ,8$. 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.

56 pages (pdflatex). Contains a .bbl file, 33 figures in pdf format, and a mathematica file triangular.m. The tex source uses IOP and tikz macros (not included). Minor changes with respect to v1. Final version published in the journal

References in corpus (7)

• Non compact conformal field theory and the a_2^{(2)} (Izergin-Korepin) model in regime III
• Critical surfaces for general bond percolation problems
• Phase diagram of the chromatic polynomial on a torus
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• Eigenvalue amplitudes of the Potts model on a torus
• Relations between Potts and RSOS models on a torus
• Integrability vs non-integrability: Hard hexagons and hard squares compared

Cited by in corpus (6)

• On the correspondence between boundary and bulk lattice models and (logarithmic) conformal field theories
• $U_q({\mathfrak{sl}}_n)$ web models and ${\mathbb{Z}}_n$ spin interfaces
• Cylinder partition function of the 6-vertex model from algebraic geometry
• The phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet
• From hard spheres to hard-core spins
• Ergodicity of the Wang--Swendsen--Kotecký algorithm on several classes of lattices on the torus