Dynamical properties of potts model with invisible states

We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. This model is regarded as a standard model to analyse nature of phase transition. We can control the energy barrier between the ordered state and disordered state without changing the symmetry which breaks at the transition point. We focus on melting process starting from the perfect ordered state. We calculate time-dependency of the order parameter, density of invisible state, and internal energy. All of them show two-step relaxation behavior. We also analyze the relationship between the characteristic melting time and characteristic scale of the energy barrier by changing the number of invisible states. We find that characteristic melting time increases as the energy barrier enlarges in this model. This model is regarded as a fundamental model to analyze dynamic behavior near the first-order phase transition point.