Non-probabilistic fermionic limit shapes
We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and arctic curves, in the absence of the next-nearest neighbor p...
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ftdatacite:10.48550/arxiv.2007.06621 2023-05-15T15:04:40+02:00 Non-probabilistic fermionic limit shapes Bocini, Saverio Stéphan, Jean-Marie 2020 https://dx.doi.org/10.48550/arxiv.2007.06621 https://arxiv.org/abs/2007.06621 unknown arXiv https://dx.doi.org/10.1088/1742-5468/abcd34 arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph FOS Physical sciences article-journal Article ScholarlyArticle Text 2020 ftdatacite https://doi.org/10.48550/arxiv.2007.06621 https://doi.org/10.1088/1742-5468/abcd34 2022-03-10T15:37:24Z We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and arctic curves, in the absence of the next-nearest neighbor perturbation. The perturbation considered turns out to not be always positive, that is, the corresponding statistical mechanical model does not always have positive Boltzmann weights. We investigate how the density profile is affected by this nonpositive perturbation. We find that in some regions, the effects of the negative signs are suppressed, and renormalize to zero. However, depending on boundary conditions, new "crazy regions" emerge, in which minus signs proliferate, and the density of fermions is not in $[0,1]$ anymore. We provide a simple intuition for such behavior, and compute exactly the density profile both on the lattice and in the scaling limit. : 23 pages, 8 figures. v2: minor improvements Article in Journal/Newspaper Arctic DataCite Metadata Store (German National Library of Science and Technology) Arctic |
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DataCite Metadata Store (German National Library of Science and Technology) |
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ftdatacite |
language |
unknown |
topic |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph FOS Physical sciences |
spellingShingle |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph FOS Physical sciences Bocini, Saverio Stéphan, Jean-Marie Non-probabilistic fermionic limit shapes |
topic_facet |
Statistical Mechanics cond-mat.stat-mech Mathematical Physics math-ph FOS Physical sciences |
description |
We study a translational invariant free fermions model in imaginary time, with nearest neighbor and next-nearest neighbor hopping terms, for a class of inhomogeneous boundary conditions. This model is known to give rise to limit shapes and arctic curves, in the absence of the next-nearest neighbor perturbation. The perturbation considered turns out to not be always positive, that is, the corresponding statistical mechanical model does not always have positive Boltzmann weights. We investigate how the density profile is affected by this nonpositive perturbation. We find that in some regions, the effects of the negative signs are suppressed, and renormalize to zero. However, depending on boundary conditions, new "crazy regions" emerge, in which minus signs proliferate, and the density of fermions is not in $[0,1]$ anymore. We provide a simple intuition for such behavior, and compute exactly the density profile both on the lattice and in the scaling limit. : 23 pages, 8 figures. v2: minor improvements |
format |
Article in Journal/Newspaper |
author |
Bocini, Saverio Stéphan, Jean-Marie |
author_facet |
Bocini, Saverio Stéphan, Jean-Marie |
author_sort |
Bocini, Saverio |
title |
Non-probabilistic fermionic limit shapes |
title_short |
Non-probabilistic fermionic limit shapes |
title_full |
Non-probabilistic fermionic limit shapes |
title_fullStr |
Non-probabilistic fermionic limit shapes |
title_full_unstemmed |
Non-probabilistic fermionic limit shapes |
title_sort |
non-probabilistic fermionic limit shapes |
publisher |
arXiv |
publishDate |
2020 |
url |
https://dx.doi.org/10.48550/arxiv.2007.06621 https://arxiv.org/abs/2007.06621 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_relation |
https://dx.doi.org/10.1088/1742-5468/abcd34 |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.2007.06621 https://doi.org/10.1088/1742-5468/abcd34 |
_version_ |
1766336400915955712 |