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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/139061
Ver los metadatos del registro completo
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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 |
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openAccess |
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