Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks

Andrea Cavagna; Antonio Culla; Luca Di Carlo; Irene Giardina; Tomas S. Grigera

doi:10.1016/j.crhy.2019.05.008

From statistical physics to social sciences / De la physique statistique aux sciences sociales

Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks
[Le ferromagnétisme marginal à basse température explique les corrélations à longue portée dans les essaims d'oiseaux]

Andrea Cavagna ¹ ; Antonio Culla ^1,² ; Luca Di Carlo ^1,² ; Irene Giardina ^1,^2,³ ; Tomas S. Grigera ^4,^5,⁶

¹ Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, 00185 Roma, Italy
² Dipartimento di Fisica, Università “La Sapienza”, 00185 Roma, Italy
³ INFN, Unità di Roma 1, 00185 Roma, Italy
⁴ Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), CONICET y Universidad Nacional de La Plata, Calle 59 no. 789, B1900BTE La Plata, Argentina
⁵ CCT CONICET La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
⁶ Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina

Comptes Rendus. Physique, Volume 20 (2019) no. 4, pp. 319-328.

Résumé
Abstract

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, $T_{c}$ , 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, $T_{c}$ , 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.

Publié le : 2019-05-01

DOI : 10.1016/j.crhy.2019.05.008

Keywords: Collective behaviour, Statistical physics, Monte Carlo simulations
Mot clés : Comportement collectif, Physique statistique, Simulation Monte-Carlo

Affiliations des auteurs :

Andrea Cavagna ¹ ; Antonio Culla ^{1, 2} ; Luca Di Carlo ^{1, 2} ; Irene Giardina ^{1, 2, 3} ; Tomas S. Grigera ^{4, 5, 6}

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     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},
}

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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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