Zhong W, Barkema GT, Panja D. Super slowing down in the bond-diluted Ising model.
Phys Rev E 2020;
102:022132. [PMID:
32942400 DOI:
10.1103/physreve.102.022132]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 08/03/2020] [Indexed: 11/07/2022]
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.
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