Arctic curves of the four-vertex model
Abstract We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states, boxed plane partitions, and fishnet diagrams in qu...
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crioppubl:10.1088/1751-8121/ad02ce 2024-09-09T19:19:24+00:00 Arctic curves of the four-vertex model Burenev, I N Colomo, F Maroncelli, A Pronko, A G Russian Science Foundation Italian Ministry of Education, University and Research 2023 http://dx.doi.org/10.1088/1751-8121/ad02ce https://iopscience.iop.org/article/10.1088/1751-8121/ad02ce https://iopscience.iop.org/article/10.1088/1751-8121/ad02ce/pdf unknown IOP Publishing https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining Journal of Physics A: Mathematical and Theoretical volume 56, issue 46, page 465202 ISSN 1751-8113 1751-8121 journal-article 2023 crioppubl https://doi.org/10.1088/1751-8121/ad02ce 2024-08-12T04:14:18Z Abstract We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states, boxed plane partitions, and fishnet diagrams in quantum field theory. In the scaling limit, the model exhibits the emergence of an arctic curve separating a central disordered region from six frozen ‘corners’ of ferroelectric or anti-ferroelectric type. We determine the analytic expression of the interface by means of the Tangent Method. We supplement this heuristic method with an alternative, rigorous derivation of the arctic curve. This is based on the exact evaluation of suitable correlation functions, devised to detect spatial transition from order to disorder, in terms of the partition function of some discrete log-gas associated to the orthogonalizing measure of the Hahn polynomials. As a by-product, we also deduce that the arctic curve’s fluctuations are governed by the Tracy–Widom distribution. Article in Journal/Newspaper Arctic IOP Publishing Arctic Journal of Physics A: Mathematical and Theoretical 56 46 465202 |
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Abstract We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states, boxed plane partitions, and fishnet diagrams in quantum field theory. In the scaling limit, the model exhibits the emergence of an arctic curve separating a central disordered region from six frozen ‘corners’ of ferroelectric or anti-ferroelectric type. We determine the analytic expression of the interface by means of the Tangent Method. We supplement this heuristic method with an alternative, rigorous derivation of the arctic curve. This is based on the exact evaluation of suitable correlation functions, devised to detect spatial transition from order to disorder, in terms of the partition function of some discrete log-gas associated to the orthogonalizing measure of the Hahn polynomials. As a by-product, we also deduce that the arctic curve’s fluctuations are governed by the Tracy–Widom distribution. |
author2 |
Russian Science Foundation Italian Ministry of Education, University and Research |
format |
Article in Journal/Newspaper |
author |
Burenev, I N Colomo, F Maroncelli, A Pronko, A G |
spellingShingle |
Burenev, I N Colomo, F Maroncelli, A Pronko, A G Arctic curves of the four-vertex model |
author_facet |
Burenev, I N Colomo, F Maroncelli, A Pronko, A G |
author_sort |
Burenev, I N |
title |
Arctic curves of the four-vertex model |
title_short |
Arctic curves of the four-vertex model |
title_full |
Arctic curves of the four-vertex model |
title_fullStr |
Arctic curves of the four-vertex model |
title_full_unstemmed |
Arctic curves of the four-vertex model |
title_sort |
arctic curves of the four-vertex model |
publisher |
IOP Publishing |
publishDate |
2023 |
url |
http://dx.doi.org/10.1088/1751-8121/ad02ce https://iopscience.iop.org/article/10.1088/1751-8121/ad02ce https://iopscience.iop.org/article/10.1088/1751-8121/ad02ce/pdf |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Journal of Physics A: Mathematical and Theoretical volume 56, issue 46, page 465202 ISSN 1751-8113 1751-8121 |
op_rights |
https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining |
op_doi |
https://doi.org/10.1088/1751-8121/ad02ce |
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Journal of Physics A: Mathematical and Theoretical |
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56 |
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46 |
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465202 |
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1809759514667253760 |