Leading birds by their beaks: The response of flocks to external perturbations

Nikos Kyriakopoulos, Francesco Ginelli*, John Toner

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)


We study the asymptotic response of polar ordered active fluids ('flocks') to small external aligning fields h. The longitudinal susceptibility x diverges, in the thermodynamic limit, like h as h → 0 . In finite systems of linear size L, x saturates to a value ∼Lγ. The universal exponents ν and γ depend only on the spatial dimensionality d, and are related to the dynamical exponent z and the 'roughness exponent' α characterizing the unperturbed flock dynamics. Using a well supported conjecture for the values of these two exponents, we obtain ν = 2/3, γ = 4/5 in d = 2 and ν = 1/4, γ = 2/5 in d= 3. These values are confirmed by our simulations.

Original languageEnglish
Article number073039
Pages (from-to)1-14
JournalNew Journal of Physics
Issue number7
Publication statusPublished - 1 Jul 2016
MoE publication typeA1 Journal article-refereed


  • active matter
  • emergent behavior
  • flocking
  • renormalization group
  • response theory

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