Study on the two-dimensional kinetic Ising model with the dynamic Monte Carlo renormalization group method

Abstract

Using a modified dynamic Monte Carlo renormalization group method, the two- dimensional kinetic Ising model is studied, and the dynamic critical exponent is obtained. The critical temperature of phase transition can be obtained by the renormalization method for the correlation function. In the method we used, the correlation function is replaced with the absolute value of the magnetization, and it is found that the evolution of the absolute value of the magnetization over time satisfies the power-law form. It is found that the value of the dynamic critical exponent tends to be a stable value in the form of a power-law function as the scale of the system increases. The dynamic critical exponent obtained is z≃2.15. When the modified dynamic Monte Carlo renormalization group method is applied to the two-dimensional Glauber model, the obtained dynamic critical exponent is z≃2.25.