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Phase-ordering kinetics on graphs.

R Burioni1, D Cassi, F Corberi

  • 1Dipartimento di Fisica and INFN, Università di Parma, Parco Area delle Scienze 7/A, I-423100 Parma, Italy.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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We numerically investigated phase-ordering kinetics in Ising models on fractal graphs. A key exponent for the integrated response function is universally independent of temperature and pinning, linked to network topology.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Network Science

Background:

  • Phase-ordering kinetics describes how systems self-organize after a rapid temperature change.
  • The Ising model is a fundamental model in statistical mechanics for studying magnetism and phase transitions.
  • Fractal structures and random networks present unique challenges for studying physical phenomena.

Purpose of the Study:

  • To numerically investigate phase-ordering kinetics in the Ising model with single spin-flip dynamics.
  • To analyze scaling properties and compute dynamical exponents on various graph structures, including fractals.
  • To identify universal behaviors in dynamical exponents, particularly for the integrated response function.

Main Methods:

  • Numerical simulations of the Ising model on diverse graph types (geometrical fractals, percolation clusters).

Related Experiment Videos

  • Application of single spin-flip dynamics to model system evolution after a temperature quench.
  • Calculation of scaling properties and dynamical exponents, including the integrated response function exponent (a_{chi}).

    • Main Results:

    • Dynamical exponents were computed for each fractal structure.
    • The exponent a_{chi} for the integrated response function was found to be independent of temperature and pinning.
    • This exponent's independence contrasts with other exponents, suggesting a universal characteristic.

    Conclusions:

    • The universal nature of a_{chi} indicates a strong connection to the topological properties of the networks.
    • This finding is analogous to observations on regular lattices, extending universality concepts.
    • The study highlights the importance of network topology in determining critical dynamical behaviors.