The six-vertex model and Schramm-Loewner evolution
| Autor: | Kenyon, Richard, Miller, Jason, Sheffield, Scott, Wilson, David B. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 95, 052146 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.95.052146 |
| Popis: | 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 6-vertex model configuration, and argue that its scaling limit is a space-filling version of the random fractal curve SLE$_\kappa$, Schramm--Loewner evolution with parameter $\kappa$, where $4<\kappa\leq 12+8\sqrt{2}$. For square ice, $\kappa=12$. At the "free-fermion point" of the 6-vertex model, $\kappa=8+4\sqrt{3}$. These unusual values lie outside the classical interval $2\le \kappa\le 8$. Comment: 5 pages, 5 figures |
| Databáze: | arXiv |
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