Non-probabilistic fermionic limit shapes

Abstract 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 n...

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Published in:Journal of Statistical Mechanics: Theory and Experiment
Main Authors: Bocini, Saverio, Stéphan, Jean-Marie
Format: Article in Journal/Newspaper
Language:unknown
Published: IOP Publishing 2021
Subjects:
Online Access:http://dx.doi.org/10.1088/1742-5468/abcd34
https://iopscience.iop.org/article/10.1088/1742-5468/abcd34
https://iopscience.iop.org/article/10.1088/1742-5468/abcd34/pdf
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spelling crioppubl:10.1088/1742-5468/abcd34 2024-06-02T08:02:08+00:00 Non-probabilistic fermionic limit shapes Bocini, Saverio Stéphan, Jean-Marie 2021 http://dx.doi.org/10.1088/1742-5468/abcd34 https://iopscience.iop.org/article/10.1088/1742-5468/abcd34 https://iopscience.iop.org/article/10.1088/1742-5468/abcd34/pdf unknown IOP Publishing https://iopscience.iop.org/page/copyright https://iopscience.iop.org/info/page/text-and-data-mining Journal of Statistical Mechanics: Theory and Experiment volume 2021, issue 1, page 013204 ISSN 1742-5468 journal-article 2021 crioppubl https://doi.org/10.1088/1742-5468/abcd34 2024-05-07T14:00:15Z Abstract 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. Article in Journal/Newspaper Arctic IOP Publishing Arctic Journal of Statistical Mechanics: Theory and Experiment 2021 1 013204
institution Open Polar
collection IOP Publishing
op_collection_id crioppubl
language unknown
description Abstract 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.
format Article in Journal/Newspaper
author Bocini, Saverio
Stéphan, Jean-Marie
spellingShingle Bocini, Saverio
Stéphan, Jean-Marie
Non-probabilistic fermionic limit shapes
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 IOP Publishing
publishDate 2021
url http://dx.doi.org/10.1088/1742-5468/abcd34
https://iopscience.iop.org/article/10.1088/1742-5468/abcd34
https://iopscience.iop.org/article/10.1088/1742-5468/abcd34/pdf
geographic Arctic
geographic_facet Arctic
genre Arctic
genre_facet Arctic
op_source Journal of Statistical Mechanics: Theory and Experiment
volume 2021, issue 1, page 013204
ISSN 1742-5468
op_rights https://iopscience.iop.org/page/copyright
https://iopscience.iop.org/info/page/text-and-data-mining
op_doi https://doi.org/10.1088/1742-5468/abcd34
container_title Journal of Statistical Mechanics: Theory and Experiment
container_volume 2021
container_issue 1
container_start_page 013204
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