Evaluation of integrals for the emptiness formation probability in the square-ice model
We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple integral representation (MIR) for the EFP can be given as a...
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2024
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ftdoajarticles:oai:doaj.org/article:9cd23550123646a089a594c44836f5ef 2024-09-09T19:25:00+00:00 Evaluation of integrals for the emptiness formation probability in the square-ice model F. Colomo A.G. Pronko 2024-07-01T00:00:00Z https://doi.org/10.1016/j.nuclphysb.2024.116565 https://doaj.org/article/9cd23550123646a089a594c44836f5ef EN eng Elsevier http://www.sciencedirect.com/science/article/pii/S0550321324001317 https://doaj.org/toc/0550-3213 0550-3213 doi:10.1016/j.nuclphysb.2024.116565 https://doaj.org/article/9cd23550123646a089a594c44836f5ef Nuclear Physics B, Vol 1004, Iss , Pp 116565- (2024) Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 article 2024 ftdoajarticles https://doi.org/10.1016/j.nuclphysb.2024.116565 2024-08-05T17:49:11Z We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple integral representation (MIR) for the EFP can be given as a finite-size matrix determinant of Fredholm type. Our conjecture is based on the explicit evaluation of the MIR for particular values of geometric parameters and on two kinds of identities for the boundary correlation function. The obtained representation can be further written as the Fredholm determinant of some linear integral operator. We show that as the geometric parameters of the EFP are tuned to the vicinity of the arctic curve arising in the scaling limit, the conjectured determinant turns into the GUE Tracy–Widom distribution. Article in Journal/Newspaper Arctic Directory of Open Access Journals: DOAJ Articles Arctic Ice Point ENVELOPE(-56.781,-56.781,51.217,51.217) Nuclear Physics B 1004 116565 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 |
spellingShingle |
Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 F. Colomo A.G. Pronko Evaluation of integrals for the emptiness formation probability in the square-ice model |
topic_facet |
Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 |
description |
We study the emptiness formation probability (EFP) in the six-vertex model with domain wall boundary conditions. We present a conjecture according to which at the ice point, i.e., when all the Boltzmann weights are equal, the known multiple integral representation (MIR) for the EFP can be given as a finite-size matrix determinant of Fredholm type. Our conjecture is based on the explicit evaluation of the MIR for particular values of geometric parameters and on two kinds of identities for the boundary correlation function. The obtained representation can be further written as the Fredholm determinant of some linear integral operator. We show that as the geometric parameters of the EFP are tuned to the vicinity of the arctic curve arising in the scaling limit, the conjectured determinant turns into the GUE Tracy–Widom distribution. |
format |
Article in Journal/Newspaper |
author |
F. Colomo A.G. Pronko |
author_facet |
F. Colomo A.G. Pronko |
author_sort |
F. Colomo |
title |
Evaluation of integrals for the emptiness formation probability in the square-ice model |
title_short |
Evaluation of integrals for the emptiness formation probability in the square-ice model |
title_full |
Evaluation of integrals for the emptiness formation probability in the square-ice model |
title_fullStr |
Evaluation of integrals for the emptiness formation probability in the square-ice model |
title_full_unstemmed |
Evaluation of integrals for the emptiness formation probability in the square-ice model |
title_sort |
evaluation of integrals for the emptiness formation probability in the square-ice model |
publisher |
Elsevier |
publishDate |
2024 |
url |
https://doi.org/10.1016/j.nuclphysb.2024.116565 https://doaj.org/article/9cd23550123646a089a594c44836f5ef |
long_lat |
ENVELOPE(-56.781,-56.781,51.217,51.217) |
geographic |
Arctic Ice Point |
geographic_facet |
Arctic Ice Point |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Nuclear Physics B, Vol 1004, Iss , Pp 116565- (2024) |
op_relation |
http://www.sciencedirect.com/science/article/pii/S0550321324001317 https://doaj.org/toc/0550-3213 0550-3213 doi:10.1016/j.nuclphysb.2024.116565 https://doaj.org/article/9cd23550123646a089a594c44836f5ef |
op_doi |
https://doi.org/10.1016/j.nuclphysb.2024.116565 |
container_title |
Nuclear Physics B |
container_volume |
1004 |
container_start_page |
116565 |
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1809894812175826944 |