Super slowing down in the bond-diluted Ising model

Abstract

In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time τ at the critical point increases with system size L in power-law fashion: τ ∼ 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 ) ∼ ( 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.