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Wei Zhong1, Gerard T Barkema1, Debabrata Panja1

  • 1Department of Information and Computing Sciences, Utrecht University, Princetonplein 5, 3584 CC Utrecht, The Netherlands.

Physical Review. E
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In statistical physics models, dynamics slow near critical points. This study reveals a "super slowing down" in the bond-diluted Ising model as it nears the percolation threshold, with a diverging dynamical critical exponent.

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Area of Science:

  • Statistical Physics
  • Dynamical Critical Phenomena

Background:

  • Dynamics in statistical physics models slow near critical points.
  • Correlation time (τ) typically scales with system size (L) as τ∼L^{z}, defining the critical dynamical exponent (z).

Purpose of the Study:

  • Investigate the dynamical critical exponent in the two-dimensional bond-diluted Ising model.
  • Analyze the behavior of the dynamical critical exponent as the percolation threshold is approached.

Main Methods:

  • Numerical analysis of the autocorrelation of total magnetization.
  • Measurement of the mean-square deviation of total magnetization.

Main Results:

  • The power-law relationship τ∼L^{z} holds for the bond-diluted Ising model (p>p_{c}).
  • The dynamical critical exponent z(p) exhibits strong dependence on bond concentration (p).
  • z(p) diverges as the percolation threshold (p_{c}=1/2) is approached: z(p)-z(1)∼(p-p_{c})^{-2}, termed 'super slowing down'.

Conclusions:

  • The bond-diluted Ising model exhibits super slowing down near the percolation threshold.
  • Anomalous diffusion in magnetization supports the observed super slowing down phenomenon.