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Numerical simulations reveal that quenched disorder in ferromagnetic Ising models leads to critical percolation structures during phase ordering. This structure evolves and compacts over time, consistent with dynamical scaling principles observed in non-disordered systems.

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Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Phase-ordering kinetics describe the evolution of systems after a quench.
  • Disorder, such as random bonds or fields, significantly impacts system dynamics.
  • Percolation theory describes the formation of clusters and networks.

Purpose of the Study:

  • To investigate the role of quenched disorder in the phase-ordering kinetics of a 2D ferromagnetic Ising model.
  • To analyze the formation and evolution of structures during the coarsening process.
  • To compare disordered systems with their non-disordered counterparts.

Main Methods:

  • Numerical simulations of the two-dimensional ferromagnetic Ising model.
  • Introduction of quenched disorder (random bonds and random fields).
  • Analysis of phase-ordering kinetics and structure formation.

Main Results:

  • A critical percolation structure emerges at an early stage of phase ordering in disordered systems.
  • This percolation structure becomes progressively more compact during the coarsening process.
  • Similar structural evolution is observed in the absence of disorder.

Conclusions:

  • Quenched disorder influences the early-stage structure formation in phase ordering.
  • The coarsening dynamics in disordered systems can be understood within a dynamical scaling framework.
  • The study highlights the interplay between disorder, percolation, and coarsening in magnetic systems.