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

TL;DR

This paper exactly determines the complex-temperature phase diagram of the 1D $Z_6$ clock model, revealing unique intersection points and connecting it to higher-dimensional models, thus providing new insights into phase boundary phenomena.

Contribution

It presents the first exact complex-temperature phase diagram of the 1D $Z_6$ clock model, highlighting a finite-$K$ intersection point and linking it to higher-dimensional models.

Findings

Identified a finite-$K$ intersection point with three curves meeting.

Established a connection between 1D and 2D $Z_6$ clock models.

Provided insights into phase boundary phenomena in statistical 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.