The arctic circle revisited
Abstract. 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 dete...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.311.972 2023-05-15T14:45:32+02:00 The arctic circle revisited F. Colomo A. G. Pronko The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.972 http://arxiv.org/pdf/0704.0362v1.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.972 http://arxiv.org/pdf/0704.0362v1.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://arxiv.org/pdf/0704.0362v1.pdf text ftciteseerx 2016-01-07T22:34:29Z Abstract. 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. 1. Text Arctic Unknown Arctic Saddle Point ENVELOPE(73.483,73.483,-53.017,-53.017) |
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Open Polar |
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Unknown |
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ftciteseerx |
language |
English |
description |
Abstract. 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. 1. |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
F. Colomo A. G. Pronko |
spellingShingle |
F. Colomo A. G. Pronko The arctic circle revisited |
author_facet |
F. Colomo A. G. Pronko |
author_sort |
F. Colomo |
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 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.972 http://arxiv.org/pdf/0704.0362v1.pdf |
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_source |
http://arxiv.org/pdf/0704.0362v1.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.311.972 http://arxiv.org/pdf/0704.0362v1.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766316940564889600 |