Ising (conformal) fields and cluster area measures

DOI10.1073/pnas.0900700106zbMath1202.82017arXiv0812.4030OpenAlexW2116676908WikidataQ37153709 ScholiaQ37153709MaRDI QIDQ3066186

Federico Camia, Charles M. Newman

Publication date: 9 January 2011

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.4030

zbMATH Keywords

continuum scaling limitSLEcritical Ising modelCLEFK clusters

Mathematics Subject Classification ID

Continuum limits in quantum field theory (81T27) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items

Pivotal, cluster, and interface measures for critical planar percolation ⋮ Conformal covariance of connection probabilities and fields in 2D critical percolation ⋮ Conformal loop ensembles and the stress-energy tensor ⋮ Critical Ising on the square lattice mixes in polynomial time ⋮ The Ising magnetization exponent on \(\mathbb{Z }^2\) is \(1/15\) ⋮ Conformal Measure Ensembles for Percolation and the FK–Ising Model ⋮ Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman ⋮ Connection probabilities and RSW‐type bounds for the two‐dimensional FK Ising model ⋮ Planar Ising magnetization field. I: Uniqueness of the critical scaling limit

Cites Work

• Asymptotics of a \(\tau\)-function arising in the two-dimensional Ising model
• The scaling limit geometry of near-critical 2D percolation
• Two-dimensional scaling limits via marked nonsimple loops
• Two-dimensional critical percolation: the full scaling limit
• Near-critical percolation in two dimensions
• Infinite conformal symmetry in two-dimensional quantum field theory
• SLEs as boundaries of clusters of Brownian loops
• Scaling limits of loop-erased random walks and uniform spanning trees
• Coloring percolation clusters at random.
• Scaling relations for 2D-percolation
• Hölder regularity and dimension bounds for random curves
• Continuum nonsimple loops and 2D critical percolation
• SLE for theoretical physicists
• On the number of incipient spanning clusters
• Inequalities with applications to percolation and reliability
• A note on percolation
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

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