The Arctic Circle Revisited
The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this correlation function is given, both in terms of certain determinant an...
| Main Authors: | , |
|---|---|
| Format: | Text |
| Language: | unknown |
| Published: |
arXiv
2007
|
| Subjects: | |
| Online Access: | https://dx.doi.org/10.48550/arxiv.0704.0362 https://arxiv.org/abs/0704.0362 |
| id |
ftdatacite:10.48550/arxiv.0704.0362 |
|---|---|
| record_format |
openpolar |
| spelling |
ftdatacite:10.48550/arxiv.0704.0362 2023-05-15T14:47:53+02:00 The Arctic Circle Revisited Colomo, F. Pronko, A. G. 2007 https://dx.doi.org/10.48550/arxiv.0704.0362 https://arxiv.org/abs/0704.0362 unknown arXiv Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ Mathematical Physics math-ph High Energy Physics - Theory hep-th FOS Physical sciences 15A52, 82B05, 82B20, 82B23 article-journal Article ScholarlyArticle Text 2007 ftdatacite https://doi.org/10.48550/arxiv.0704.0362 2022-04-01T15:31:54Z The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this correlation function is given, both in terms of certain determinant and multiple integral, which allows for a systematic treatment of the limit shapes of the model for full range of values of vertex weights. Specifically, we show that for vertex weights corresponding to the free-fermion line on the phase diagram, the emptiness formation probability is related to a one-matrix model with a triple logarithmic singularity, or Triple Penner model. The saddle-point analysis of this model leads to the Arctic Circle Theorem, and its generalization to the Arctic Ellipses, known previously from domino tilings. : 16 pages, 3 figures Text Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic Saddle Point ENVELOPE(73.483,73.483,-53.017,-53.017) |
| institution |
Open Polar |
| collection |
DataCite Metadata Store (German National Library of Science and Technology) |
| op_collection_id |
ftdatacite |
| language |
unknown |
| topic |
Mathematical Physics math-ph High Energy Physics - Theory hep-th FOS Physical sciences 15A52, 82B05, 82B20, 82B23 |
| spellingShingle |
Mathematical Physics math-ph High Energy Physics - Theory hep-th FOS Physical sciences 15A52, 82B05, 82B20, 82B23 Colomo, F. Pronko, A. G. The Arctic Circle Revisited |
| topic_facet |
Mathematical Physics math-ph High Energy Physics - Theory hep-th FOS Physical sciences 15A52, 82B05, 82B20, 82B23 |
| description |
The problem of limit shapes in the six-vertex model with domain wall boundary conditions is addressed by considering a specially tailored bulk correlation function, the emptiness formation probability. A closed expression of this correlation function is given, both in terms of certain determinant and multiple integral, which allows for a systematic treatment of the limit shapes of the model for full range of values of vertex weights. Specifically, we show that for vertex weights corresponding to the free-fermion line on the phase diagram, the emptiness formation probability is related to a one-matrix model with a triple logarithmic singularity, or Triple Penner model. The saddle-point analysis of this model leads to the Arctic Circle Theorem, and its generalization to the Arctic Ellipses, known previously from domino tilings. : 16 pages, 3 figures |
| format |
Text |
| author |
Colomo, F. Pronko, A. G. |
| author_facet |
Colomo, F. Pronko, A. G. |
| author_sort |
Colomo, F. |
| title |
The Arctic Circle Revisited |
| title_short |
The Arctic Circle Revisited |
| title_full |
The Arctic Circle Revisited |
| title_fullStr |
The Arctic Circle Revisited |
| title_full_unstemmed |
The Arctic Circle Revisited |
| title_sort |
arctic circle revisited |
| publisher |
arXiv |
| publishDate |
2007 |
| url |
https://dx.doi.org/10.48550/arxiv.0704.0362 https://arxiv.org/abs/0704.0362 |
| long_lat |
ENVELOPE(73.483,73.483,-53.017,-53.017) |
| geographic |
Arctic Saddle Point |
| geographic_facet |
Arctic Saddle Point |
| genre |
Arctic |
| genre_facet |
Arctic |
| op_rights |
Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ |
| op_doi |
https://doi.org/10.48550/arxiv.0704.0362 |
| _version_ |
1766318987886460928 |