Dynamical properties of Potts model with invisible states

TL;DR

This paper investigates the dynamic melting process of the Potts model with invisible states near a first-order phase transition, revealing how energy barriers influence relaxation times and providing insights into phase transition dynamics.

Contribution

It introduces a detailed analysis of the dynamic behavior of the Potts model with invisible states, highlighting the relationship between energy barriers and melting times without altering symmetry.

Findings

Two-step relaxation behavior observed in order parameter and energy.

Melting time increases with the size of the energy barrier.

Model serves as a fundamental framework for phase transition dynamics.

Abstract

We study dynamic behavior of Potts model with invisible states near the first-order phase transition temperature. We focus on melting process starting from the perfect ordered state. This model is regarded as a standard model to analyze nature of phase transition. We can control the energy barrier between the ordered state and paramagnetic state without changing the symmetry which breaks at the transition point. We calculate time-dependency of the order parameter, density of invisible state, and internal energy. They show two-step relaxation behavior. We also consider the relation 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. Thus, this model is regarded as a fundamental model to analyze dynamic behavior near the first-order phase transition point.