[Le ferromagnétisme marginal à basse température explique les corrélations à longue portée dans les essaims d'oiseaux]
Nous introduisons un nouveau modèle ferromagnétique capable de reproduire l'une des propriétés les plus intrigantes du comportement collectif des essaims d'oiseaux, à savoir le fait qu'un ordre collectif fort coexiste avec des corrélations sans échelle du module des degrés de liberté microscopiques, à savoir les vitesses des oiseaux. L'idée-clé de la nouvelle théorie est que le potentiel à un corps nécessaire pour lier le module des degrés de liberté microscopiques autour d'une valeur finie est marginal, c'est-à-dire qu'il a une courbure nulle. Nous étudions le modèle en utilisant l'approximation du champ moyen et les simulations de Monte-Carlo en trois dimensions, complétées par l'analyse à l'échelle finie. Alors qu'à la température critique standard, , les propriétés du modèle marginal sont exactement les mêmes que celles d'un ferromagnétique normal avec rupture de symétrie continue, nos résultats montrent qu'un nouveau point critique à température nulle émerge, de sorte que, dans sa phase profondément ordonnée, le modèle marginal développe une susceptibilité divergente et une longueur de corrélation du module des degrés de liberté microscopiques, en analogie complète avec les données expérimentales sur des essaims naturels d'oiseaux.
We introduce a new ferromagnetic model capable of reproducing one of the most intriguing properties of collective behaviour in starling flocks, namely the fact that strong collective order coexists with scale-free correlations of the modulus of the microscopic degrees of freedom, that is, the birds' speeds. The key idea of the new theory is that the single-particle potential needed to bound the modulus of the microscopic degrees of freedom around a finite value is marginal, that is, it has zero curvature. We study the model by using mean-field approximation and Monte Carlo simulations in three dimensions, complemented by finite-size scaling analysis. While at the standard critical temperature, , the properties of the marginal model are exactly the same as a normal ferromagnet with continuous symmetry breaking, our results show that a novel zero-temperature critical point emerges, so that in its deeply ordered phase the marginal model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in complete analogy with experimental data on natural flocks of starlings.
Mot clés : Comportement collectif, Physique statistique, Simulation Monte-Carlo
Andrea Cavagna 1 ; Antonio Culla 1, 2 ; Luca Di Carlo 1, 2 ; Irene Giardina 1, 2, 3 ; Tomas S. Grigera 4, 5, 6
@article{CRPHYS_2019__20_4_319_0,
author = {Andrea Cavagna and Antonio Culla and Luca Di Carlo and Irene Giardina and Tomas S. Grigera},
title = {Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks},
journal = {Comptes Rendus. Physique},
pages = {319--328},
publisher = {Elsevier},
volume = {20},
number = {4},
year = {2019},
doi = {10.1016/j.crhy.2019.05.008},
language = {en},
}
TY - JOUR AU - Andrea Cavagna AU - Antonio Culla AU - Luca Di Carlo AU - Irene Giardina AU - Tomas S. Grigera TI - Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks JO - Comptes Rendus. Physique PY - 2019 SP - 319 EP - 328 VL - 20 IS - 4 PB - Elsevier DO - 10.1016/j.crhy.2019.05.008 LA - en ID - CRPHYS_2019__20_4_319_0 ER -
%0 Journal Article %A Andrea Cavagna %A Antonio Culla %A Luca Di Carlo %A Irene Giardina %A Tomas S. Grigera %T Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks %J Comptes Rendus. Physique %D 2019 %P 319-328 %V 20 %N 4 %I Elsevier %R 10.1016/j.crhy.2019.05.008 %G en %F CRPHYS_2019__20_4_319_0
Andrea Cavagna; Antonio Culla; Luca Di Carlo; Irene Giardina; Tomas S. Grigera. Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks. Comptes Rendus. Physique, Volume 20 (2019) no. 4, pp. 319-328. doi : 10.1016/j.crhy.2019.05.008. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2019.05.008/
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