Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model
arXiv:2403.02086 · doi:10.1103/PhysRevLett.133.258301
Abstract
We investigate the scaling behavior of Nambu-Goldstone (NG) modes in the ordered phase of the Vicsek model, introducing a phenomenological equation of motion (EOM) incorporating a previously overlooked non-linear term. This term arises from the interaction between velocity fields and density fluctuations, leading to new scaling behaviors. We derive exact scaling exponents in two dimensions, which reproduce the isotropic scaling behavior reported in a prior numerical simulation.
5 pages, 1 figure. This paper is a revised version of arXiv:2401.01603 with modified derivation of the scaling exponents
References in corpus (28)
- Novel type of phase transition in a system of self-driven particles
- Flocks, herds, and schools: A quantitative theory of flocking
- Onset of collective and cohesive motion
- The nonperturbative functional renormalization group and its applications
- Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
- A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
- Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria
- Sound waves and the absence of Galilean invariance in flocks
- Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
- Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
- Asymmetric exchange in flocks
- Long-range Order and Directional Defect Propagation in the Nonreciprocal XY Model with Vision Cone Interactions
- Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting
- Quantitative Assessment of the Toner and Tu Theory of Polar Flocks
- Giant fluctuations and structural effects in a flocking epithelium
- Two-dimensional crystals far from equilibrium
- Existence of long-range order in the steady state of a two dimensional, two-temperature XY model
- Metastability of Constant-Density Flocks
- Incompressible polar active fluids in the moving phase
- Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
- Correlated Noise and Critical Dimensions
- Harmonic chain far from equilibrium: single-file diffusion, long-range order, and hyperuniformity
- Evidence of fluctuation-induced first-order phase transition in active matter
- A new universality class describes Vicsek's flocking phase in physical dimensions
- Phase Diagram for a 2-D Two-Temperature Diffusive XY Model
- Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
- Continuous symmetry breaking of low-dimensional systems driven by inhomogeneous oscillatory driving forces
- Scaling behaviour of non-equilibrium planar -atic spin systems under weak fluctuations