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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Published in:Journal of Statistical Mechanics: Theory and Experiment
Main Authors: Bocini, Saverio, Stéphan, Jean-Marie
Other Authors: Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Probabilités, statistique, physique mathématique (PSPM), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Università degli Studi di Firenze = University of Florence = Université de Florence (UniFI), ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018)
Format: Report
Language:English
Published: HAL CCSD 2020
Subjects:
Online Access:https://hal.science/hal-02933352
https://doi.org/10.1088/1742-5468/abcd34
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spelling ftunivlyon:oai:HAL:hal-02933352v1 2024-09-09T19:25:28+00:00 Non-probabilistic fermionic limit shapes Bocini, Saverio Stéphan, Jean-Marie Institut Camille Jordan (ICJ) École Centrale de Lyon (ECL) Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS) Probabilités, statistique, physique mathématique (PSPM) Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL) Università degli Studi di Firenze = University of Florence = Université de Florence (UniFI) ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018) 2020-09-08 https://hal.science/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.science/hal-02933352 ARXIV: 2007.06621 doi:10.1088/1742-5468/abcd34 https://hal.science/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 ftunivlyon https://doi.org/10.1088/1742-5468/abcd34 2024-07-08T23:59:53Z 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 Université de Lyon: HAL Arctic Journal of Statistical Mechanics: Theory and Experiment 2021 1 013204
institution Open Polar
collection Université de Lyon: HAL
op_collection_id ftunivlyon
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 (ICJ)
École Centrale de Lyon (ECL)
Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL)
Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)
Probabilités, statistique, physique mathématique (PSPM)
Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)
Università degli Studi di Firenze = University of Florence = Université de Florence (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.science/hal-02933352
https://doi.org/10.1088/1742-5468/abcd34
geographic Arctic
geographic_facet Arctic
genre Arctic
genre_facet Arctic
op_source https://hal.science/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.science/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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