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, Tomas Sebastian; 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.
Fil: Cavagna, Andrea. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
Fil: Di Carlo, Luca. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
Fil: Giardina, Irene. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale Di Fisica Nucleare.; Italia
Fil: Grandinetti, Luca. Dipartimento di Scienza Applicata e Tecnologia; Italia
Fil: Grigera, Tomas Sebastian. 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. Centro Científico Tecnológico Mendoza. Museo de Ciencias Naturales y Antropológicas J. Cornelio Moyano; Argentina
Fil: Pisegna, Giulia. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
Materia
collective behavior
swarming
renormalization group
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:11336/125630
Acceder
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spelling Renormalization group crossover in the critical dynamics of field theories with mode coupling termsCavagna, AndreaDi Carlo, LucaGiardina, IreneGrandinetti, LucaGrigera, Tomas SebastianPisegna, Giuliacollective behaviorswarmingrenormalization grouphttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1Motivated 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.Fil: Cavagna, Andrea. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; ItaliaFil: Di Carlo, Luca. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; ItaliaFil: Giardina, Irene. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale Di Fisica Nucleare.; ItaliaFil: Grandinetti, Luca. Dipartimento di Scienza Applicata e Tecnologia; ItaliaFil: Grigera, Tomas Sebastian. 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. Centro Científico Tecnológico Mendoza. Museo de Ciencias Naturales y Antropológicas J. Cornelio Moyano; ArgentinaFil: Pisegna, Giulia. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; ItaliaAmerican Physical Society2019-12-23info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/125630Cavagna, Andrea; Di Carlo, Luca; Giardina, Irene; Grandinetti, Luca; Grigera, Tomas Sebastian; et al.; Renormalization group crossover in the critical dynamics of field theories with mode coupling terms; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 100; 6; 23-12-2019; 62130-621302470-00452470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevE.100.062130info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.062130info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:54:40Zoai:ri.conicet.gov.ar:11336/125630instacron: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:34982025-11-12 09:54:40.391CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
collective behavior
swarming
renormalization group
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, Tomas Sebastian
Pisegna, Giulia
author Cavagna, Andrea
author_facet Cavagna, Andrea
Di Carlo, Luca
Giardina, Irene
Grandinetti, Luca
Grigera, Tomas Sebastian
Pisegna, Giulia
author_role author
author2 Di Carlo, Luca
Giardina, Irene
Grandinetti, Luca
Grigera, Tomas Sebastian
Pisegna, Giulia
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv collective behavior
swarming
renormalization group
topic collective behavior
swarming
renormalization group
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
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.
Fil: Cavagna, Andrea. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
Fil: Di Carlo, Luca. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
Fil: Giardina, Irene. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia. Istituto Nazionale Di Fisica Nucleare.; Italia
Fil: Grandinetti, Luca. Dipartimento di Scienza Applicata e Tecnologia; Italia
Fil: Grigera, Tomas Sebastian. 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. Centro Científico Tecnológico Mendoza. Museo de Ciencias Naturales y Antropológicas J. Cornelio Moyano; Argentina
Fil: Pisegna, Giulia. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; Italia
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 2019-12-23
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/11336/125630
Cavagna, Andrea; Di Carlo, Luca; Giardina, Irene; Grandinetti, Luca; Grigera, Tomas Sebastian; et al.; Renormalization group crossover in the critical dynamics of field theories with mode coupling terms; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 100; 6; 23-12-2019; 62130-62130
2470-0045
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125630
identifier_str_mv Cavagna, Andrea; Di Carlo, Luca; Giardina, Irene; Grandinetti, Luca; Grigera, Tomas Sebastian; et al.; Renormalization group crossover in the critical dynamics of field theories with mode coupling terms; American Physical Society; Physical Review E: Statistical, Nonlinear and Soft Matter Physics; 100; 6; 23-12-2019; 62130-62130
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/url/https://link.aps.org/doi/10.1103/PhysRevE.100.062130
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.062130
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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