Properties of classical clock models and possibilities for their quantum simulation*

The q-state clock model is a classical spin model that corresponds to the Ising model (when q = 2) and the XY model (when q goes to infinity). The integer-q clock model has been studied extensively and has been shown to have a single phase transition when q = 2,3,4 and two phase transitions when q > 4. We investigate a class of clock models for non-integer q using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with non-integer q has two phase transitions with one of them possibly in the Ising universality class. In this model, thermodynamic quantities appear to vary smoothly with q as q approaches an integer from below. However, the appearance of an additional spin state when q crosses an integer results in an abrupt change in the thermodynamic quantities. The model with non-integer q serves as a testbed for TRG methods and has interesting features which already appear at small lattice sizes, making this model a candidate for study on near-term quantum simulators and in particular Rydberg atom devices.