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 2D 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 pdependence. Moreover, we show numerically that z(p), as obtained from the autocorrelation of the total magnetisation, 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 magnetisation, which exhibits anomalous diffusion at the critical point, supports this result.