Partial Order in Potts Models on the Generalized Decorated Square Lattice

We explore the Potts model on the generalized decorated square lattice, with both nearest (J₁) and next-nearest (J₂) neighbor interactions. Using the tensor renormalization-group method augmented by higher order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J₂/J₁. There is no finite-temperature transition for the q = 4 case when J₁ = J₂, whereas the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.