Super slowing down in the bond-diluted Ising model

In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time tau at the critical point increases with system size L in power-law fashion: tau similar to L-z, which defines the critical dynamical exponent z. We show that this also holds for the two-dimensional bond-diluted Ising model in the regime p > p(c), where p is the parameter denoting the bond concentration, but with a dynamical critical exponent z(p) which shows a strong p dependence. Moreover, we show numerically that z(p), as obtained from the autocorrelation of the total magnetization, diverges when the percolation threshold p(c) = 1/2 is approached: z(p) - z(1) similar to (p - p(c))(-2). We refer to this observed extremely fast increase of the correlation time with size as super slowing down. Independent measurement data from the mean-square deviation of the total magnetization, which exhibits anomalous diffusion at the critical point, support this result.