Six-vertex model and Schramm-Loewner evolution
Name
PhysRevE.95.052146.pdf
Size
344.65 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Kenyon, Richard
Miller, Jason
Wilson, David B.
Sheffield, Scott Roger
Date Issued
May 2017
Journal
Physical Review E
Publisher
American Physical Society
Citation
Kenyon, Richard et al. “Six-Vertex Model and Schramm-Loewner Evolution.” Physical Review E 95.5 (2017): n. pag. © 2017 American Physical Society
Version
Final published version
Abstract
Square ice is a statistical mechanics model for two-dimensional ice, widely believed to have a conformally invariant scaling limit. We associate a Peano (space-filling) curve to a square ice configuration, and more generally to a so-called six-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SLE[subscript κ], Schramm-Loewner evolution with parameter κ, where 4 < κ ≤ 12 + 8 √2. For square ice, κ = 12. At the “free-fermion point” of the six-vertex model, κ = 8 + 4√3. These unusual values lie outside the classical interval 2≤κ≤8.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.95.052146
