Sharpness of the phase transition in percolation models

1987/09/01 by Michael Aizenman, David J. Barsky · 10 citations
Mathematics · Physics and Astronomy · #Combinatorics #Condensed matter physics #Critical exponent #Electrical resistivity and conductivity #Extrapolation #Geometry #Invariant (physics) #Ising model #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Percolation (cognitive psychology) #Percolation critical exponents #Percolation threshold #Phase transition #Physics #Quantum mechanics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · doi:10.1007/bf01212322

crossref issued 1987/09/01 · crossref published 1987/09/01 · crossref published-print 1987/09/01 · openalex publication_date 1987/09/01 · crossref created 2005/02/25 · crossref deposited 2019/05/02 · openalex created_date 2025/10/10 · crossref indexed 2026/07/13 · openalex updated_date 2026/07/23

Citations

• On the critical behavior of the magnetization in high-dimensional Ising models
• Percolation Theory for Mathematicians

Cited by

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• Sharp thresholds and percolation in the plane
• Critical percolation of virtually free groups and other tree-like graphs
• A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model
• Scaling relations for 2D-percolation
• Phase transition for percolation on a randomly stretched lattice
• Phase Separation in Random Cluster Models III: Circuit Regularity
• Phase transitions on nonamenable graphs
• A coarse graining for the Fortuin–Kasteleyn measure in random media
• Confidence intervals for the critical value in the divide and color model
• Percolation theory [wikipedia]