Classical analog of quantum models in synthetic dimensions

We introduce a classical analog of quantum matter in ultracold molecule-synthetic or Rydberg atom-synthetic dimensions, by extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying its finite-temperature properties. For intermediate values of J1, the resulting phases and phase diagrams are similar to those of the clock and Villain models, in which three phases emerge. There exists a sheet phase analogous to that found in quantum synthetic dimension models between the high-temperature disordered phase and the low-temperature ferromagnetic phase. We also employ machine learning to uncover nontrivial features of the phase diagram using the learning by confusion approach, which is able to discern several successive phase transitions.