1997/03/07 by Andras Czirok, András Czirók, H. Eugene Stanley +2 · 7 citations
Biochemistry, Genetics and Molecular Biology · Environmental Science · Mathematics · Physics and Astronomy · #Amplitude #Condensed matter physics #Constant (computer programming) #Critical line #Diffusion and Search Dynamics #Ecosystem dynamics and resilience #Function (biology) #Geometry #Mathematics #Micro and Nano Robotics #Monte Carlo method #Noise (video) #Parameter space #Phase (matter) #Phase diagram #Physics #Plane (geometry) #Power law #Quantum mechanics #Range (aeronautics) #Statistical physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/0305-4470/30/5/009
published as J. Phys. A: Math. Gen. 30 1375-1385 (1997)
openalex publication_date 1997/03/07 · arxiv created 2006/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a biologically inspired, inherently non-equilibrium model consisting of self-propelled particles. In the model, particles move on a plane with a velocity of constant magnitude; they locally interact with their neighbours by choosing at each timestep a velocity direction equal to the average direction of their neighbours. Thus, in the limit of vanishing velocities the model becomes analogous to a Monte Carlo realization of the classical XY ferromagnet. We show by large-scale numerical simulations that, unlike in the equilibrium XY model, a long-range ordered phase characterized by non-vanishing net flow, , emerges in this system in a phase-space domain bordered by a critical line along which the fluctuations of the order parameter diverge. The corresponding phase diagram as a function of two parameters, the amplitude of noise and the average density of the particles is calculated and is found to have the form . We also find that scales as a function of the external bias h (field or `wind') according to a power law . In the ordered phase the system shows long-range correlated fluctuations and 1/f noise.