Ordering process in the kinetic Ising model on the honeycomb lattice

The ordering process after quenching from infinite temperature is studied in the kinetic Ising model on the honeycomb lattice below the critical temperature by means of Monte Carlo simulations. Because of the presence of metastable droplets on the honeycomb lattice, the time scale of ordering becomes very long at low temperatures. Due to the metastability, the time evolution of magnetization per site, m(t), seems to be scaled by a characteristic time scale exp(2K)L-2t for large L. Here, K, L, and t denote the nearest-neighbor coupling divided by the temperature, the linear dimension of the system, and the time after the quenching, respectively.