dc.contributor.author | Kenyon, Richard | |
dc.contributor.author | Miller, Jason | |
dc.contributor.author | Wilson, David B. | |
dc.contributor.author | Sheffield, Scott Roger | |
dc.date.accessioned | 2017-06-08T18:35:01Z | |
dc.date.available | 2017-06-08T18:35:01Z | |
dc.date.issued | 2017-05 | |
dc.date.submitted | 2016-05 | |
dc.identifier.issn | 2470-0045 | |
dc.identifier.issn | 2470-0053 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/109751 | |
dc.description.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. | en_US |
dc.description.sponsorship | Simons Foundation (Grant 306120) | en_US |
dc.description.sponsorship | National Science Foundation (U.S.) (Grant DMS-1209044) | en_US |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (Grants EP/L018896/1) | en_US |
dc.description.sponsorship | Engineering and Physical Sciences Research Council (Grants EP/I03372X/1) | en_US |
dc.publisher | American Physical Society | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1103/PhysRevE.95.052146 | en_US |
dc.rights | 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. | en_US |
dc.source | American Physical Society | en_US |
dc.title | Six-vertex model and Schramm-Loewner evolution | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Kenyon, Richard et al. “Six-Vertex Model and Schramm-Loewner Evolution.” Physical Review E 95.5 (2017): n. pag. © 2017 American Physical Society | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.contributor.mitauthor | Sheffield, Scott Roger | |
dc.relation.journal | Physical Review E | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2017-06-02T16:41:11Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | American Physical Society | |
dspace.orderedauthors | Kenyon, Richard; Miller, Jason; Sheffield, Scott; Wilson, David B. | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-5951-4933 | |
mit.license | PUBLISHER_POLICY | en_US |