A Bond-Weighted Tensor Renormalization Group Study of the q-State Ferromagnetic Potts Models on the Square Lattice

It has been proven that the phase transition of the q-state ferromagnetic Potts model on the square lattice is of the second order for. However, some observables of the model show features of a first-order phase transition. In particular, a recent large-scale Monte Carlo investigation of the 4-state Potts model observed that the two-peak structure of the energy density distribution becomes more noticeable when L increases. This finding suggests that the signal of coexistence of phases grows stronger with L. Motivated by these unusual critical behaviors, we study the energy density E and the specific heat of the 4-state Potts model on the square lattice using the technique of bond-weighted tensor renormalization group (BTRG). As a comparison, we also investigate the and ferromagnetic Potts models on the square lattice using the same method. Remarkably, our results imply that there may be a small energy gap for the model. Although the appearance of the small energy gap can be explained and would disappear with a more sophisticated investigation, our finding suggests that further investigation is required to determine whether a message of a first-order phase transition is genuine or an artificial effect.