The influence of the Wolff cluster structure on the determination of the critical dynamic exponent

Recently we reported some interesting features of the Wolff algorithm behaviour when applied to the site-bond-correlated Ising model. Our main results were that a stronger correlation diminishes the autocorrelation time but it does not change or affect the critical dynamic exponent. In this work, we analyse the Wolff cluster structure and how it varies with the spatial correlation. The fractal dimensions are determined for several values of the magnetic atom concentration and spatial correlation, giving an estimation of the Wolff critical dynamic exponent.