Non-probabilistic fermionic limit shapes
23 pages, 8 figures 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 nex...
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ftccsdartic:oai:HAL:hal-02933352v1 2023-05-15T15:05:15+02:00 Non-probabilistic fermionic limit shapes Bocini, Saverio Stéphan, Jean-Marie Institut Camille Jordan Villeurbanne (ICJ) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université Jean Monnet Saint-Étienne (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) Probabilités, statistique, physique mathématique (PSPM) Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL) Università degli Studi di Firenze = University of Florence Firenze (UNIFI) ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018) 2020-09-08 https://hal.archives-ouvertes.fr/hal-02933352 https://doi.org/10.1088/1742-5468/abcd34 en eng HAL CCSD info:eu-repo/semantics/altIdentifier/arxiv/2007.06621 info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/abcd34 hal-02933352 https://hal.archives-ouvertes.fr/hal-02933352 ARXIV: 2007.06621 doi:10.1088/1742-5468/abcd34 https://hal.archives-ouvertes.fr/hal-02933352 2020 [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] info:eu-repo/semantics/preprint Preprints, Working Papers, . 2020 ftccsdartic https://doi.org/10.1088/1742-5468/abcd34 2021-12-12T01:17:26Z 23 pages, 8 figures 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. Report Arctic Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Arctic Journal of Statistical Mechanics: Theory and Experiment 2021 1 013204 |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] |
spellingShingle |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] Bocini, Saverio Stéphan, Jean-Marie Non-probabilistic fermionic limit shapes |
topic_facet |
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] [PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] |
description |
23 pages, 8 figures 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. |
author2 |
Institut Camille Jordan Villeurbanne (ICJ) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université Jean Monnet Saint-Étienne (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) Probabilités, statistique, physique mathématique (PSPM) Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL) Università degli Studi di Firenze = University of Florence Firenze (UNIFI) ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018) |
format |
Report |
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 |
HAL CCSD |
publishDate |
2020 |
url |
https://hal.archives-ouvertes.fr/hal-02933352 https://doi.org/10.1088/1742-5468/abcd34 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
https://hal.archives-ouvertes.fr/hal-02933352 2020 |
op_relation |
info:eu-repo/semantics/altIdentifier/arxiv/2007.06621 info:eu-repo/semantics/altIdentifier/doi/10.1088/1742-5468/abcd34 hal-02933352 https://hal.archives-ouvertes.fr/hal-02933352 ARXIV: 2007.06621 doi:10.1088/1742-5468/abcd34 |
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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1766336981573304320 |