Complex-temperature phase diagram of Potts and RSOS models

Abstract

We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A\_{p-1} type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N -> infinity, of partition function zeros for p=4,5,6,infinity and L=2,3,4 and study selected features for p>6 and/or L>4. This information enables us to formulate several conjectures about the thermodynamic limit, L -> infinity, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p=4). We show how this feature is modified by taking fixed transverse boundary conditions.

60 pages, 16 figures, 2 tables

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Cited by in corpus (13)

• Integrable Floquet dynamics
• A Little Statistical Mechanics for the Graph Theorist
• Counting colored planar maps: algebraicity results
• Phase diagram of the chromatic polynomial on a torus
• Character decomposition of Potts model partition functions. I. Cyclic geometry
• Measuring complex partition function zeroes of Ising models in quantum simulators
• Q-colourings of the triangular lattice: Exact exponents and conformal field theory
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. VI. Square lattice with special boundary conditions
• Phase diagram of the triangular-lattice Potts antiferromagnet
• A generalized Beraha conjecture for non-planar graphs
• Character decomposition of Potts model partition functions. II. Toroidal geometry
• Duality and Fisher zeros in the 2D Potts model on square lattice
• Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions