Abstract. We study dynamic behavior of Potts model with invisible states near the firstorder 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.
IntroductionFrustration causes many interesting static and dynamic behavior which are not observed in unfrustrated systems because of peculiar density of states [1][2][3][4][5][6][7][8][9][10]. In two-dimensional frustrated systems, there have been found many nontrivial phase transitions such as order by disorder [11,12], reentrant phase transition [13][14][15][16][17], topological phase transition [18], and novel type of first-order phase transition. Recently, strange first-order phase transitions have been found in two-dimensional frustrated continuous spin systems [19][20][21][22].In [19], the authors studied equilibrium properties of the classical Heisenberg model on triangular lattice with nearest neighbor ferromagnetic interaction J 1 and third-nearest neighbor antiferromagnetic interaction J 3 . They found that a first-order phase transition with threefold symmetry breaking occurs at finite temperature. This looks a strange phase transition, since phase transition with threefold symmetry breaking is often second-order phase transition on two-dimensional lattice e.g. the three-state ferromagnetic Potts model [23]. After this study, similar nature of first-order phase transition have been found by a number of researchers [20][21][22]. Stoudenmire et al. found a first-order phase transition with breaking of threefold symmetry in J 1 − J 3 model with biquadratic interaction on triangular lattice. Okumura et al. also found