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

Abstract

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 x 0 separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

Critical exponents testing of a random number generator with the Wolff cluster algorithm

“…Theoretically, the dynamics of a statistical system would be more sensitive to anomalies in a PRNG as such anomalies could be averaged out in static quantities of the system. One would expect a more pronounced showing of anomalies of a PRNG in a dynamic process; for example, the FSS of the autocorrelation time or the dynamic exponent [55,56]. However, unlike static scaling, which has exact theoretical scaling exponents or coefficient values, dynamics scaling theory does not provide theoretical values for scaling exponents such as the dynamic exponent [19].…”