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Updated: Jul 26, 2025
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
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Cluster percolation in the two-dimensional Ising spin glass.
1Institut für Physik, Technische Universität Chemnitz, 09107 Chemnitz, Germany.
Physical Review. E
|June 17, 2023
Summary
Researchers explored spin glass models using Monte Carlo simulations. They found that replica overlap clusters, crucial for spin glass transitions, exhibit percolation thresholds that decrease with system size, supporting a zero-temperature transition theory.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Computational Physics
Background:
- Ordering transitions in spin systems are often described as geometric percolation phenomena.
- A direct connection between percolation and spin glasses with quenched disorder remains incompletely established, with limited numerical evidence.
Purpose of the Study:
- To investigate the percolation properties of various cluster types in the 2D Edwards-Anderson Ising spin-glass model.
- To establish a connection between percolation and the spin-glass transition using numerical simulations.
Main Methods:
- Monte Carlo simulations were employed to study cluster percolation.
- Analysis focused on Fortuin-Kasteleyn-Coniglio-Klein clusters and replica overlap clusters.
Main Results:
- Fortuin-Kasteleyn-Coniglio-Klein clusters percolate at a non-zero temperature, consistent with predictions on the Nishimori line.
- Replica overlap clusters show percolation thresholds that decrease with increasing system size, aligning with a zero-temperature spin-glass transition in 2D.
- A link was found between overlap and the density difference of the two largest clusters.
Conclusions:
- The study supports a model where the spin-glass transition emerges from a density difference of the largest clusters within the percolating phase.
- Percolation of replica overlap clusters provides crucial insight into the nature of spin-glass transitions in disordered systems.
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