The Percolation Signature of the Spin Glass Transition

Abstract

Magnetic ordering at low temperature for Ising ferromagnets manifests itself within the associated Fortuin-Kasteleyn (FK) random cluster representation as the occurrence of a single positive density percolating network. In this paper we investigate the percolation signature for Ising spin glass ordering -- both in short-range (EA) and infinite-range (SK) models -- within a two-replica FK representation and also within the different Chayes-Machta-Redner two-replica graphical representation. Based on numerical studies of the $\pm J$ EA model in three dimensions and on rigorous results for the SK model, we conclude that the spin glass transition corresponds to the appearance of {\it two} percolating clusters of {\it unequal} densities.

arXiv comment13 pages, 6 figures

References in corpus (11)

• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• New algorithm and results for the three-dimensional random field Ising Model
• Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and Universality
• Replica Monte Carlo Simulation (Revisited)
• Graphical Representations for Ising Systems in External Fields
• Graphical representations and cluster algorithms for critical points with fields
• Cluster Monte Carlo algorithms for diluted spin glasses

Cited by in corpus (19)

• The critical behavior of three-dimensional Ising spin glass models
• Critical parameters of the three-dimensional Ising spin glass
• Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension
• Matching microscopic and macroscopic responses in glasses
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Cluster Percolation in the Two-Dimensional Ising Spin Glass
• Percolation of Fortuin-Kasteleyn clusters for the random-bond Ising model
• Lattice Percolation Approach to 3D Modeling of Tissue Aging
• Geometric clusters in the overlap of the Ising model
• Spin glasses and percolation
• Massively parallel simulations for disordered systems
• Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model
• Force network analysis of jammed solids
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model
• Avoiding critical slowdown in models with SALR interactions
• Random-cluster correlation inequalities for Gibbs fields
• Rate-Equation Modelling and Ensemble Approach to Extraction of Parameters for Viral Infection-Induced Cell Apoptosis and Necrosis
• FKG (and other inequalities) via (generalized) FK representation (and iterated folding)
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman