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.