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Related Experiment Video

Updated: Mar 30, 2026

Tuning the Contractility and Deformation Modes of Active Actin-Based Assemblies In Vitro: From Two-Dimensional Active Networks to Liquid Crystal Drops
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Flocking with discrete symmetry: The two-dimensional active Ising model.

A P Solon1, J Tailleur1

  • 1Université Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75205 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
PubMed
Summary
This summary is machine-generated.

This study reveals that collective motion in the active Ising model is a liquid-gas phase transition. The phase diagram exhibits a critical point belonging to the Ising universality class.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Non-equilibrium Systems

Background:

  • The active Ising model describes systems with self-propelled particles exhibiting collective motion.
  • Emergent collective behavior arises from spontaneous symmetry breaking and ferromagnetic alignment.
  • Understanding phase transitions in non-equilibrium systems is crucial for diverse fields.

Purpose of the Study:

  • To analyze the active Ising model as a minimal flocking model with discrete rotational symmetry.
  • To characterize the transition to collective motion as a liquid-gas phase transition.
  • To investigate the phase diagram and critical phenomena in different ensembles.

Main Methods:

  • Detailed analysis of the active Ising model on a two-dimensional lattice.
  • Investigation in the density-velocity and density-temperature parameter planes.
  • Development of a continuum theory to model microscopic behavior.
  • Analytical prediction of phase diagram features and coexistence properties.

Main Results:

  • The transition to collective motion is identified as a liquid-gas phase transition.
  • A critical point in the density-velocity plane belongs to the Ising universality class.
  • The density-temperature phase diagram shows the critical point shifted to infinite density, precluding a supercritical region.
  • The continuum theory accurately reproduces the model's behavior, predicting phase diagram shapes and coexistence properties.

Conclusions:

  • The active Ising model provides a minimal framework for studying flocking and liquid-gas transitions.
  • Symmetry differences between phases prevent a supercritical region in the canonical ensemble.
  • Analytical predictions from the continuum theory validate the microscopic model's findings.