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Cluster percolation in the three-dimensional ±J random-bond Ising model.

L Münster1, M Weigel1,2

  • 1Technische Universität Chemnitz, Institut für Physik, 09107 Chemnitz, Germany.

Physical Review. E
|March 20, 2026
PubMed
Summary
This summary is machine-generated.

This study explores cluster percolation and ordering in a 3D random-bond Ising model. A novel percolation signature for thermodynamic transitions was identified, linked to two equal-density clusters.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The relationship between cluster percolation and thermodynamic ordering is crucial in disordered magnetic systems.
  • The three-dimensional ±J random-bond Ising model serves as a fundamental framework for studying these phenomena.
  • Understanding how antiferromagnetic bonds influence these transitions is key to characterizing complex magnetic phases.

Purpose of the Study:

  • To investigate the connection between cluster percolation and equilibrium ordering in the 3D ±J random-bond Ising model.
  • To analyze the impact of varying antiferromagnetic bond fractions on percolation and thermodynamic transitions.
  • To identify and characterize percolation signatures associated with ferromagnetic and spin-glass phase transitions.

Main Methods:

  • Extensive parallel-tempering Monte Carlo simulations were employed.
  • Cluster definitions were explored, primarily in the space of overlaps between two independent system replicas.
  • Scaling behavior at secondary percolation transitions was compared with thermodynamic phase transition behavior.

Main Results:

  • In the pure ferromagnet, the percolation point aligns with the thermodynamic ordering transition.
  • For disordered ferromagnets and spin-glass phases, a distinct percolation transition occurs above the ordering point, marked by two equal-density percolating clusters.
  • The densities of these two clusters diverge precisely at the lower (disordered) ferromagnetic or spin-glass transition points, indicating a percolation signature.

Conclusions:

  • A novel percolation signature for thermodynamic ordering transitions in disordered magnetic systems has been identified.
  • The study establishes a clear link between the emergence of two percolating clusters and the onset of ferromagnetic and spin-glass phases.
  • The findings provide a new method for characterizing phase transitions in complex magnetic materials through percolation analysis.