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Persistence in one-dimensional Ising models with parallel dynamics.

G I Menon1, P Ray, P Shukla

  • 1The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600 113, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
PubMed
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We investigated spin persistence in one-dimensional Ising models. The probability of a spin remaining unchanged decays over time, with the exponent precisely determined through a novel mapping to particle annihilation models.

Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Ising models are fundamental in statistical mechanics for understanding magnetism.
  • Parallel dynamics introduce unique behaviors in spin systems.
  • Persistence phenomena explore the long-term stability of system states.

Purpose of the Study:

  • To analyze the persistence probability in one-dimensional Ising models with parallel dynamics.
  • To determine the exact exponent governing the decay of spin persistence.
  • To investigate dynamical scaling in persistent site distributions.

Main Methods:

  • Numerical simulations of ferromagnetic and antiferromagnetic one-dimensional Ising models.
  • Analysis of spin flip probabilities over time from random initial configurations.

Related Experiment Videos

  • Mapping the system dynamics to two decoupled A+A-->0 annihilation models.
  • Finite size scaling analysis to understand dynamical scaling properties.

    • Main Results:

    • The probability of a spin remaining unchanged decays as P(t) ~ 1/t^theta(p).
    • Numerical analysis yielded theta(p) approximately 0.75.
    • The mapping to A+A-->0 models provided an exact solution: theta(p) = 3/4.
    • Finite size scaling confirmed the nature of dynamical scaling.

    Conclusions:

    • The persistence exponent in these Ising models is precisely 3/4.
    • The A+A-->0 model provides an accurate theoretical framework for this dynamics.
    • Understanding persistence is crucial for characterizing the long-term behavior of magnetic systems.