Six-vertex model and Schramm-Loewner evolution
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 l...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/109751 https://orcid.org/0000-0002-5951-4933 |
| _version_ | 1811079537401790464 |
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| author | Kenyon, Richard Miller, Jason Wilson, David B. Sheffield, Scott Roger |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kenyon, Richard Miller, Jason Wilson, David B. Sheffield, Scott Roger |
| author_sort | Kenyon, Richard |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:16:38Z |
| format | Article |
| id | mit-1721.1/109751 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:16:38Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1097512022-10-01T02:31:53Z Six-vertex model and Schramm-Loewner evolution Kenyon, Richard Miller, Jason Wilson, David B. Sheffield, Scott Roger Massachusetts Institute of Technology. Department of Mathematics Sheffield, Scott Roger 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. Simons Foundation (Grant 306120) National Science Foundation (U.S.) (Grant DMS-1209044) Engineering and Physical Sciences Research Council (Grants EP/L018896/1) Engineering and Physical Sciences Research Council (Grants EP/I03372X/1) 2017-06-08T18:35:01Z 2017-06-08T18:35:01Z 2017-05 2016-05 2017-06-02T16:41:11Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/109751 Kenyon, Richard et al. “Six-Vertex Model and Schramm-Loewner Evolution.” Physical Review E 95.5 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-5951-4933 en http://dx.doi.org/10.1103/PhysRevE.95.052146 Physical Review E 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Kenyon, Richard Miller, Jason Wilson, David B. Sheffield, Scott Roger Six-vertex model and Schramm-Loewner evolution |
| title | Six-vertex model and Schramm-Loewner evolution |
| title_full | Six-vertex model and Schramm-Loewner evolution |
| title_fullStr | Six-vertex model and Schramm-Loewner evolution |
| title_full_unstemmed | Six-vertex model and Schramm-Loewner evolution |
| title_short | Six-vertex model and Schramm-Loewner evolution |
| title_sort | six vertex model and schramm loewner evolution |
| url | http://hdl.handle.net/1721.1/109751 https://orcid.org/0000-0002-5951-4933 |
| work_keys_str_mv | AT kenyonrichard sixvertexmodelandschrammloewnerevolution AT millerjason sixvertexmodelandschrammloewnerevolution AT wilsondavidb sixvertexmodelandschrammloewnerevolution AT sheffieldscottroger sixvertexmodelandschrammloewnerevolution |