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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 .

Mn-doped zinc oxide (ZnO:Mn) thin films with low resistivity and relatively high transparency were firstly prepared on glass substrate by direct current (DC) magnetron sputtering at room temperature. Influence of film thickness on the properties of ZnO:Mn films was investigated. X-ray diffraction (XRD) and scanning electron microscopy (SEM) show that all the deposited films are polycrystalline with a hexagonal structure and have a preferred orientation along the c -axis perpendicular to the substrate. As the thickness increases from 144 to 479 nm, the crystallite size increases while the electrical resistivity decreases. However, as the thickness increases from 479 to 783 nm, the crystallite size decreases and the electrical resistivity increases. When film thickness is 479 nm, the deposited films have the lowest resistivity of 2.1 × 10 − 4 Ω cm and a relatively high transmittance of above 84% in the visible range.