  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.
