Delocalization of Uniform Graph Homomorphisms from Z2 to Z
Abstract Graph homomorphisms from the $${\mathbb {Z}}^d$$ Z d...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2021
|
| Online Access: | https://hdl.handle.net/1721.1/133144 |
| _version_ | 1826208432544284672 |
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| author | Chandgotia, Nishant Peled, Ron Sheffield, Scott Tassy, Martin |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Chandgotia, Nishant Peled, Ron Sheffield, Scott Tassy, Martin |
| author_sort | Chandgotia, Nishant |
| collection | MIT |
| description | Abstract
Graph homomorphisms from the
$${\mathbb {Z}}^d$$
Z
d
lattice to
$${\mathbb {Z}}$$
Z
are functions on
$${\mathbb {Z}}^d$$
Z
d
whose gradients equal one in absolute value. These functions are the height functions corresponding to proper 3-colorings of
$${\mathbb {Z}}^d$$
Z
d
and, in two dimensions, corresponding to the 6-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered. |
| first_indexed | 2024-09-23T14:05:40Z |
| format | Article |
| id | mit-1721.1/133144 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:05:40Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1331442023-06-28T19:58:42Z Delocalization of Uniform Graph Homomorphisms from Z2 to Z Chandgotia, Nishant Peled, Ron Sheffield, Scott Tassy, Martin Massachusetts Institute of Technology. Department of Mathematics Abstract Graph homomorphisms from the $${\mathbb {Z}}^d$$ Z d lattice to $${\mathbb {Z}}$$ Z are functions on $${\mathbb {Z}}^d$$ Z d whose gradients equal one in absolute value. These functions are the height functions corresponding to proper 3-colorings of $${\mathbb {Z}}^d$$ Z d and, in two dimensions, corresponding to the 6-vertex model (square ice). We consider the uniform model, obtained by sampling uniformly such a graph homomorphism subject to boundary conditions. Our main result is that the model delocalizes in two dimensions, having no translation-invariant Gibbs measures. Additional results are obtained in higher dimensions and include the fact that every Gibbs measure which is ergodic under even translations is extremal and that these Gibbs measures are stochastically ordered. 2021-10-27T15:32:26Z 2021-10-27T15:32:26Z 2021-09-13 2021-09-21T03:23:09Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133144 Chandgotia, Nishant, Peled, Ron, Sheffield, Scott and Tassy, Martin. 2021. "Delocalization of Uniform Graph Homomorphisms from Z2 to Z." en https://doi.org/10.1007/s00220-021-04181-0 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Chandgotia, Nishant Peled, Ron Sheffield, Scott Tassy, Martin Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title | Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title_full | Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title_fullStr | Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title_full_unstemmed | Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title_short | Delocalization of Uniform Graph Homomorphisms from Z2 to Z |
| title_sort | delocalization of uniform graph homomorphisms from z2 to z |
| url | https://hdl.handle.net/1721.1/133144 |
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