Partial order in Potts models on the generalized decorated square lattice

TL;DR

This paper investigates the phase behavior of the Potts model on a generalized decorated square lattice, revealing partial order, degeneracy, and criticality at zero temperature across different q states using advanced tensor methods.

Contribution

It introduces a tensor renormalization-group approach to analyze the Potts model on a complex lattice, highlighting partial order and critical phenomena not previously characterized.

Findings

q=2 results match exact solutions

Partial order observed for q=3 with zero entropy

Model is critical at zero temperature for q=4

Abstract

We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-neighbor (J2) 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, but the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.