2007/06/30 by Jonathan Machta, J. Machta, C. M. Newman +2 · 29 citations
Mathematics · Physics and Astronomy · #Cluster (spacecraft) #Complex Network Analysis Techniques #Computer science #Condensed matter physics #Ferromagnetism #Geometry #Ising model #Ising spin #Magnetic field #Magnetization #Mathematics #Percolation (cognitive psychology) #Percolation threshold #Physics #Quantum mechanics #Replica #Representation (politics) #Signature (topology) #Spin (aerodynamics) #Spin glass #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Thermodynamics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-007-9446-2
published in Journal of Statistical Physics 130(1), 113-128 (Springer Science+Business Media) · 13 pages, 6 figures
arxiv created 2007/06/30 · openalex publication_date 2007/10/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ± 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.