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Area of Science:

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

Background:

  • Active Ising Models (AIMs) describe systems of self-propelled particles exhibiting collective motion.
  • Spontaneous breaking of discrete symmetry is a key mechanism for flocking behavior in these models.

Purpose of the Study:

  • To apply Doi-Peliti field theory to study various AIMs and derive their hydrodynamic equations.
  • To investigate the transition from isotropic to flocked states and analyze exceptions.
  • To explore the connection between AIMs and equilibrium universality classes in the zero self-propulsion limit.

Main Methods:

  • Doi-Peliti field theory approach.
  • Derivation of hydrodynamic equations for different microscopic aligning processes.
  • Analysis of noise terms and hydrodynamic limits.
  • Field-theoretic study of zero self-propulsion limit and connection to Model C.

Main Results:

  • Hydrodynamic equations confirm known results at the deterministic level and allow for systematic inclusion of noise.
  • All studied AIMs, except for pairwise local alignment, show a first-order transition to flocking for non-zero self-propulsion.
  • The pairwise local alignment variant fails to produce flocking, explained by hydrodynamic scaling.
  • AIMs without self-propulsion, while out of equilibrium, are shown to lie outside the Model C universality class due to a distinct dynamical symmetry.

Conclusions:

  • Doi-Peliti field theory provides a powerful framework for studying AIMs and their collective behaviors.
  • The transition to flocking is robust across different AIMs, with specific microscopic details determining exceptions.
  • AIMs without self-propulsion exhibit unique non-equilibrium dynamics distinct from equilibrium universality classes like Model C.