Dynamical renormalization group for mode-coupling field theories with solenoidal constraint

Autores
Cavagna, Andrea; Di Carlo, Luca; Giardina, Irene; Grigera, Tomás Sebastián; Pisegna, Giulia; Scandolo, Mattia
Año de publicación
2021
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles' velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields - density, velocity and spin - has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.
Instituto de Física de Líquidos y Sistemas Biológicos
Materia
Física
Dynamic renormalization group
Mode-coupling
Solenoidal field
Collective behaviour
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/145809

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spelling Dynamical renormalization group for mode-coupling field theories with solenoidal constraintCavagna, AndreaDi Carlo, LucaGiardina, IreneGrigera, Tomás SebastiánPisegna, GiuliaScandolo, MattiaFísicaDynamic renormalization groupMode-couplingSolenoidal fieldCollective behaviourThe recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles' velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields - density, velocity and spin - has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.Instituto de Física de Líquidos y Sistemas Biológicos2021-08-28info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/145809enginfo:eu-repo/semantics/altIdentifier/issn/0022-4715info:eu-repo/semantics/altIdentifier/issn/1572-9613info:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-021-02800-7info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:32:22Zoai:sedici.unlp.edu.ar:10915/145809Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:32:22.99SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
title Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
spellingShingle Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
Cavagna, Andrea
Física
Dynamic renormalization group
Mode-coupling
Solenoidal field
Collective behaviour
title_short Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
title_full Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
title_fullStr Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
title_full_unstemmed Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
title_sort Dynamical renormalization group for mode-coupling field theories with solenoidal constraint
dc.creator.none.fl_str_mv Cavagna, Andrea
Di Carlo, Luca
Giardina, Irene
Grigera, Tomás Sebastián
Pisegna, Giulia
Scandolo, Mattia
author Cavagna, Andrea
author_facet Cavagna, Andrea
Di Carlo, Luca
Giardina, Irene
Grigera, Tomás Sebastián
Pisegna, Giulia
Scandolo, Mattia
author_role author
author2 Di Carlo, Luca
Giardina, Irene
Grigera, Tomás Sebastián
Pisegna, Giulia
Scandolo, Mattia
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Física
Dynamic renormalization group
Mode-coupling
Solenoidal field
Collective behaviour
topic Física
Dynamic renormalization group
Mode-coupling
Solenoidal field
Collective behaviour
dc.description.none.fl_txt_mv The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles' velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields - density, velocity and spin - has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.
Instituto de Física de Líquidos y Sistemas Biológicos
description The recent inflow of empirical data about the collective behaviour of strongly correlated biological systems has brought field theory and the renormalization group into the biophysical arena. Experiments on bird flocks and insect swarms show that social forces act on the particles' velocity through the generator of its rotations, namely the spin, indicating that mode-coupling field theories are necessary to reproduce the correct dynamical behaviour. Unfortunately, a theory for three coupled fields - density, velocity and spin - has a prohibitive degree of intricacy. A simplifying path consists in getting rid of density fluctuations by studying incompressible systems. This requires imposing a solenoidal constraint on the primary field, an unsolved problem even for equilibrium mode-coupling theories. Here, we perform an equilibrium dynamic renormalization group analysis of a mode-coupling field theory subject to a solenoidal constraint; using the classification of Halperin and Hohenberg, we can dub this case as a solenoidal Model G. We demonstrate that the constraint produces a new vertex that mixes static and dynamical coupling constants, and that this vertex is essential to grant the closure of the renormalization group structure and the consistency of dynamics with statics. Interestingly, although the solenoidal constraint leads to a modification of the static universality class, we find that it does not change the dynamical universality class, a result that seems to represent an exception to the general rule that dynamical universality classes are narrower than static ones. Our results constitute a solid stepping stone in the admittedly large chasm towards developing an off-equilibrium mode-coupling theory of biological groups.
publishDate 2021
dc.date.none.fl_str_mv 2021-08-28
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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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://sedici.unlp.edu.ar/handle/10915/145809
url http://sedici.unlp.edu.ar/handle/10915/145809
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0022-4715
info:eu-repo/semantics/altIdentifier/issn/1572-9613
info:eu-repo/semantics/altIdentifier/doi/10.1007/s10955-021-02800-7
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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reponame_str SEDICI (UNLP)
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instname_str Universidad Nacional de La Plata
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institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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