Renormalization group crossover in the critical dynamics of field theories with mode coupling terms

Autores
Cavagna, Andrea; Di Carlo, Luca; Giardina, Irene; Grandinetti, Luca; Grigera, Tomás Sebastián; Pisegna, Giulia
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Motivated by the collective behavior of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. Under a fixed-network approximation, we perform a dynamical renormalization group calculation at one loop in the near-critical disordered region, and we show that the violation of momentum conservation generates a crossover between an unstable fixed point, characterized by a dynamic critical exponent z = d/2, and a stable fixed point with z = 2. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent κ = 4/d. The crossover is regulated by a conservation length scale R0, given by the ratio between the transport coefficient and the effective friction, which is larger as the dissipation is smaller: Beyond R0, the stable fixed point dominates, while at shorter distances dynamics is ruled by the unstable fixed point and critical exponent, a behavior which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents z = 3/2 and z = 2 in the critical slowdown of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step toward reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases.
Instituto de Física de Líquidos y Sistemas Biológicos
Materia
Ciencias Exactas
Física
Biología
biological swarms
dynamics of field theories
dissipation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/139061

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spelling Renormalization group crossover in the critical dynamics of field theories with mode coupling termsCavagna, AndreaDi Carlo, LucaGiardina, IreneGrandinetti, LucaGrigera, Tomás SebastiánPisegna, GiuliaCiencias ExactasFísicaBiologíabiological swarmsdynamics of field theoriesdissipationMotivated by the collective behavior of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. Under a fixed-network approximation, we perform a dynamical renormalization group calculation at one loop in the near-critical disordered region, and we show that the violation of momentum conservation generates a crossover between an unstable fixed point, characterized by a dynamic critical exponent z = d/2, and a stable fixed point with z = 2. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent κ = 4/d. The crossover is regulated by a conservation length scale R0, given by the ratio between the transport coefficient and the effective friction, which is larger as the dissipation is smaller: Beyond R0, the stable fixed point dominates, while at shorter distances dynamics is ruled by the unstable fixed point and critical exponent, a behavior which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents z = 3/2 and z = 2 in the critical slowdown of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step toward reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases.Instituto de Física de Líquidos y Sistemas Biológicos2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf062130-062130http://sedici.unlp.edu.ar/handle/10915/139061enginfo:eu-repo/semantics/altIdentifier/issn/2470-0045info:eu-repo/semantics/altIdentifier/issn/2470-0053info:eu-repo/semantics/altIdentifier/doi/10.1103/physreve.100.062130info:eu-repo/semantics/altIdentifier/arxiv/1905.01228info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:31:53Zoai:sedici.unlp.edu.ar:10915/139061Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:31:53.354SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
title Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
spellingShingle Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
Cavagna, Andrea
Ciencias Exactas
Física
Biología
biological swarms
dynamics of field theories
dissipation
title_short Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
title_full Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
title_fullStr Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
title_full_unstemmed Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
title_sort Renormalization group crossover in the critical dynamics of field theories with mode coupling terms
dc.creator.none.fl_str_mv Cavagna, Andrea
Di Carlo, Luca
Giardina, Irene
Grandinetti, Luca
Grigera, Tomás Sebastián
Pisegna, Giulia
author Cavagna, Andrea
author_facet Cavagna, Andrea
Di Carlo, Luca
Giardina, Irene
Grandinetti, Luca
Grigera, Tomás Sebastián
Pisegna, Giulia
author_role author
author2 Di Carlo, Luca
Giardina, Irene
Grandinetti, Luca
Grigera, Tomás Sebastián
Pisegna, Giulia
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Ciencias Exactas
Física
Biología
biological swarms
dynamics of field theories
dissipation
topic Ciencias Exactas
Física
Biología
biological swarms
dynamics of field theories
dissipation
dc.description.none.fl_txt_mv Motivated by the collective behavior of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. Under a fixed-network approximation, we perform a dynamical renormalization group calculation at one loop in the near-critical disordered region, and we show that the violation of momentum conservation generates a crossover between an unstable fixed point, characterized by a dynamic critical exponent z = d/2, and a stable fixed point with z = 2. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent κ = 4/d. The crossover is regulated by a conservation length scale R0, given by the ratio between the transport coefficient and the effective friction, which is larger as the dissipation is smaller: Beyond R0, the stable fixed point dominates, while at shorter distances dynamics is ruled by the unstable fixed point and critical exponent, a behavior which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents z = 3/2 and z = 2 in the critical slowdown of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step toward reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases.
Instituto de Física de Líquidos y Sistemas Biológicos
description Motivated by the collective behavior of biological swarms, we study the critical dynamics of field theories with coupling between order parameter and conjugate momentum in the presence of dissipation. Under a fixed-network approximation, we perform a dynamical renormalization group calculation at one loop in the near-critical disordered region, and we show that the violation of momentum conservation generates a crossover between an unstable fixed point, characterized by a dynamic critical exponent z = d/2, and a stable fixed point with z = 2. Interestingly, the two fixed points have different upper critical dimensions. The interplay between these two fixed points gives rise to a crossover in the critical dynamics of the system, characterized by a crossover exponent κ = 4/d. The crossover is regulated by a conservation length scale R0, given by the ratio between the transport coefficient and the effective friction, which is larger as the dissipation is smaller: Beyond R0, the stable fixed point dominates, while at shorter distances dynamics is ruled by the unstable fixed point and critical exponent, a behavior which is all the more relevant in finite-size systems with weak dissipation. We run numerical simulations in three dimensions and find a crossover between the exponents z = 3/2 and z = 2 in the critical slowdown of the system, confirming the renormalization group results. From the biophysical point of view, our calculation indicates that in finite-size biological groups mode coupling terms in the equation of motion can significantly change the dynamical critical exponents even in the presence of dissipation, a step toward reconciling theory with experiments in natural swarms. Moreover, our result provides the scale within which fully conservative Bose-Einstein condensation is a good approximation in systems with weak symmetry-breaking terms violating number conservation, as quantum magnets or photon gases.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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/10915/139061
url http://sedici.unlp.edu.ar/handle/10915/139061
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/2470-0045
info:eu-repo/semantics/altIdentifier/issn/2470-0053
info:eu-repo/semantics/altIdentifier/doi/10.1103/physreve.100.062130
info:eu-repo/semantics/altIdentifier/arxiv/1905.01228
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/4.0/
Creative Commons Attribution 4.0 International (CC BY 4.0)
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062130-062130
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instname:Universidad Nacional de La Plata
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repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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