Partial order and finite-temperature phase transitions in Potts models on irregular lattices.

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union-Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature phase transition to a partially ordered state. From the thermodynamics of Potts models on the diced and centered diced lattices, we propose that finite-temperature transitions and partially ordered states are ubiquitous on irregular lattices.