Complex-Temperature Phase Diagram of the 1D $Z_6$ Clock Model and its Connection with Higher-Dimensional Models

Abstract

We determine the exact complex-temperature (CT) phase diagram of the 1D $Z_6$ clock model. This is of interest because it is the first exactly solved system with a CT phase boundary exhibiting a finite-$K$ intersection point where an odd number of curves (namely, three) meet, and yields a deeper insight into this phenomenon. Such intersection points occur in the 3D spin 1/2 Ising model and appear to occur in the 2D spin 1 Ising model. Further, extending our earlier work on the higher-spin Ising model, we point out an intriguing connection between the CT phase diagrams for the 1D and 2D $Z_6$ clock models.

10 pages, latex, with two epsf figures

References in corpus (8)

• Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice
• Complex-Temperature Properties of the 2D Ising Model for Nonzero Magnetic Field
• Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal Lattices
• Complex-Temperature Properties of the 2D Ising Model with $\beta H=\pm i\pi /2$
• Complex-Temperature Singularities in the $d=2$ Ising Model. II. Triangular Lattice
• Complex-Temperature Singularities in the $d=2$ Ising Model. III. Honeycomb Lattice
• A Connection Between Complex-Temperature Properties of the 1D and 2D Spin $s$ Ising Model
• Zeros of the Partition Function for Higher--Spin 2D Ising Models

Cited by in corpus (5)

• Chromatic Polynomials for Families of Strip Graphs and their Asymptotic Limits
• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit
• The Yang Lee Edge Singularity on Feynman Diagrams
• Ramified partition algebras