The Ising magnetization exponent on \(\mathbb{Z }^2\) is \(1/15\)

DOI10.1007/s00440-013-0526-8zbMath1307.82004arXiv1205.6612OpenAlexW2465023833MaRDI QIDQ466896

Christophe Garban, Charles M. Newman, Federico Camia

Publication date: 31 October 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6612

zbMATH Keywords

percolationIsing modelaverage magnetization

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items

Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd, Planar random-cluster model: scaling relations, Critical behavior of the annealed Ising model on random regular graphs, Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman, Polynomial chaos and scaling limits of disordered systems, FK-Ising coupling applied to near-critical planar models, Planar Ising magnetization field. I: Uniqueness of the critical scaling limit

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical point inequalities and scaling limits
• The Fourier spectrum of critical percolation
• Smirnov's fermionic observable away from criticality
• Critical exponents for two-dimensional percolation
• Scaling relations for 2D-percolation
• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model. II
• Planar Ising magnetization field. I: Uniqueness of the critical scaling limit
• Planar Ising correlations.
• The Romance of the Ising Model
• Towards Conformal Invariance and a Geometric Representation of the 2D Ising Magnetization Field
• Ising (conformal) fields and cluster area measures
• Connection probabilities and RSW‐type bounds for the two‐dimensional FK Ising model
• Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results
• The Random-Cluster Model
• The Spontaneous Magnetization of a Two-Dimensional Ising Model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Planar Ising magnetization field. II: Properties of the critical and near-critical scaling limits