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Six-vertex model and Schramm-Loewner evolution

Author(s)
Kenyon, Richard; Miller, Jason; Wilson, David B.; Sheffield, Scott Roger
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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.
Date issued
2017-05
URI
http://hdl.handle.net/1721.1/109751
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
2470-0045
2470-0053

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