Dynamic critical index of the Swendsen–Wang algorithm by dynamic finite-size scaling

In this work we have considered the dynamic scaling relation of the magnetization in order to study the dynamic scaling behavior of 2- and 3-dimensional Ising models. We have used the literature values of the magnetic critical exponents to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. In this way we have calculated the dynamic critical exponent Z for 2- and 3-dimensional Ising Models by using the Swendsen–Wang cluster algorithm. We have also presented that this method opens the possibility of calculating z   and x0x0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.