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1/f noise in the Ising model.

Rahul Chhimpa1, Avinash Chand Yadav1

  • 1Banaras Hindu University, Department of Physics, Institute of Science, Varanasi 221 005, India.

Physical Review. E
|August 1, 2025
PubMed
Summary
This summary is machine-generated.

Simulations of the critical Ising model reveal that temporal correlations in spin flips exhibit 1/f noise. This critical slowing down poses challenges for achieving equilibrium in spin configuration simulations.

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Area of Science:

  • Statistical physics
  • Computational physics

Background:

  • The critical Ising model is a fundamental model in statistical physics used to study phase transitions.
  • Glauber dynamics is a common method for simulating spin systems, but can suffer from critical slowing down.

Purpose of the Study:

  • To investigate temporal correlations in the N-spin critical Ising model simulated with Glauber dynamics.
  • To characterize the nature of these correlations and their impact on system equilibration.

Main Methods:

  • Simulated the N-spin critical Ising model on a square lattice using Glauber dynamics.
  • Defined a unit of time as N single-spin-flip attempts.
  • Analyzed temporal correlations in accepted spin flips and their power spectral density.

Main Results:

  • Observed a signature of nontrivial long-time correlations in accepted spin flips.
  • Demonstrated that these correlations decay logarithmically over time.
  • Found that the power spectral density follows canonical 1/f noise.

Conclusions:

  • Critical slowing down in the Ising model leads to temporally correlated spin configurations.
  • The observed 1/f noise indicates a challenge for efficient equilibration in such simulations.
  • Understanding these correlations is crucial for accurate modeling of critical phenomena.