Statistical properties of the relaxation processes of metastable states in the kinetic Ising model

Relaxation processes from a metastably ordered state in an unfavorable field to the stable equilibrium state are studied in the two-dimensional Ising model with use of the Ising Machine m-TIS2. The field and size dependence of the relaxation processes are studied by examining the statistical properties of the ensemble of time-evolution paths of the magnetization, {m(t)}. Two different types of relaxation processes are found, whose dynamics are qualitatively different from each other. For example, the ratio of the mean to the variance of the relaxation times of the metastable state changes considerably and also the shape of the distribution of relaxation times changes drastically. A remarkable similarity is found between the shapes of the m(t)'s in spite of the large scatter in the relaxation times, which suggests the existence of a kind of dynamical potential of one degree of freedom. Based on this potential picture, we analyze the distribution of relaxation times of these two processes and introduce the notion of a dynamical spinodal point for the marginal point which differs from the ordinary spinodal points found in the mean-field approximation or in the thermodynamic potential for finite systems.