Complex-temperature phase diagram of the 1D Z₆ clock model and its connection with higher-dimensional models

We determine the exact complex-temperature (CT) phase diagram of the 1D Z₆, 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 ID and 2D Z₆, clock models.