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Updated: Feb 28, 2026

Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Six-vertex model and Schramm-Loewner evolution
Richard Kenyon1, Jason Miller2, Scott Sheffield3
1Department of Mathematics, Brown University, 1 Prospect Street, Providence, Rhode Island 02912, USA.
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_{κ}, Schramm-Loewner evolution with parameter κ, where 4<κ≤12+8sqrt[2]. For square ice, κ=12. At the "free-fermion point" of the six-vertex model, κ=8+4sqrt[3]. These unusual values lie outside the classical interval 2≤κ≤8.
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