Renormalization group study of marginal ferromagnetism

Autores
Cavagna, Andrea; Culla, Antonio; Grigera, Tomas Sebastian
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension dc=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>dc. The numerical data fully confirm our theoretical results.
Fil: Cavagna, Andrea. Consiglio Nazionale delle Ricerche; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale di Fisica Nucleare; Italia
Fil: Culla, Antonio. Consiglio Nazionale delle Ricerche; Italia
Fil: Grigera, Tomas Sebastian. Consiglio Nazionale delle Ricerche; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata; Argentina
Materia
flocking
speed control
renormalization
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/212672
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Renormalization group study of marginal ferromagnetismCavagna, AndreaCulla, AntonioGrigera, Tomas Sebastianflockingspeed controlrenormalizationhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension dc=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>dc. The numerical data fully confirm our theoretical results.Fil: Cavagna, Andrea. Consiglio Nazionale delle Ricerche; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale di Fisica Nucleare; ItaliaFil: Culla, Antonio. Consiglio Nazionale delle Ricerche; ItaliaFil: Grigera, Tomas Sebastian. Consiglio Nazionale delle Ricerche; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata; ArgentinaAmerican Physical Society2022-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/212672Cavagna, Andrea; Culla, Antonio; Grigera, Tomas Sebastian; Renormalization group study of marginal ferromagnetism; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 106; 5; 11-2022; 54136-541362470-00452470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.106.054136info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.054136info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:50:39Zoai:ri.conicet.gov.ar:11336/212672instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:50:39.27CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Renormalization group study of marginal ferromagnetism
title Renormalization group study of marginal ferromagnetism
spellingShingle Renormalization group study of marginal ferromagnetism
Cavagna, Andrea
flocking
speed control
renormalization
title_short Renormalization group study of marginal ferromagnetism
title_full Renormalization group study of marginal ferromagnetism
title_fullStr Renormalization group study of marginal ferromagnetism
title_full_unstemmed Renormalization group study of marginal ferromagnetism
title_sort Renormalization group study of marginal ferromagnetism
dc.creator.none.fl_str_mv Cavagna, Andrea
Culla, Antonio
Grigera, Tomas Sebastian
author Cavagna, Andrea
author_facet Cavagna, Andrea
Culla, Antonio
Grigera, Tomas Sebastian
author_role author
author2 Culla, Antonio
Grigera, Tomas Sebastian
author2_role author
author
dc.subject.none.fl_str_mv flocking
speed control
renormalization
topic flocking
speed control
renormalization
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension dc=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>dc. The numerical data fully confirm our theoretical results.
Fil: Cavagna, Andrea. Consiglio Nazionale delle Ricerche; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale di Fisica Nucleare; Italia
Fil: Culla, Antonio. Consiglio Nazionale delle Ricerche; Italia
Fil: Grigera, Tomas Sebastian. Consiglio Nazionale delle Ricerche; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata; Argentina
description When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equations at one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension dc=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>dc. The numerical data fully confirm our theoretical results.
publishDate 2022
dc.date.none.fl_str_mv 2022-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/212672
Cavagna, Andrea; Culla, Antonio; Grigera, Tomas Sebastian; Renormalization group study of marginal ferromagnetism; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 106; 5; 11-2022; 54136-54136
2470-0045
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/212672
identifier_str_mv Cavagna, Andrea; Culla, Antonio; Grigera, Tomas Sebastian; Renormalization group study of marginal ferromagnetism; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 106; 5; 11-2022; 54136-54136
2470-0045
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.106.054136
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.106.054136
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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