The Ising model in our dimension and our times

DOI10.4171/ICM2022/200arXiv2207.03874OpenAlexW4389820321MaRDI QIDQ6200332

Andrei Okounkov

Publication date: 22 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.03874

zbMATH Keywords

phase transitionsIsing modelPotts modelmathematical modelling

Mathematics Subject Classification ID

Philosophy of mathematics (00A30) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Cites Work

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• Continuity of the phase transition for planar random-cluster and Potts models with \({1 \leq q \leq 4}\)
• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model
• The self-dual point of the two-dimensional random-cluster model is critical for \(q \geqslant 1\)
• Correlation inequalities on some partially ordered sets
• Random currents expansion of the Ising model
• Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model. II
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• Discrete holomorphicity and quantized affine algebras
• Lectures on the Ising and Potts Models on the Hypercubic Lattice
• Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
• Investigation of Gibbsian States for Three-Dimensional Lattice Systems
• Percolation
• Divergence of the correlation length for critical planar FK percolation with 1 ⩽q⩽ 4 via parafermionic observables
• Lectures on the integrability of the 6-vertex model
• Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$
• SIXTY YEARS OF PERCOLATION
• Conformal invariance of lattice models

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