Loscar Ernesto S, Baglietto Gabriel, Vazquez Federico
Instituto de Física de Líquidos y Sistemas Biológicos (IFLYSIB), UNLP, CCT La Plata-CONICET, Calle 59 no. 789, B1900BTE La Plata, Argentina.
Instituto de Cálculo, FCEN, Universidad de Buenos Aires and CONICET, C1428EGA Buenos Aires, Argentina.
Phys Rev E. 2021 Sep;104(3-1):034111. doi: 10.1103/PhysRevE.104.034111.
We study a model for the collective behavior of self-propelled particles subject to pairwise copying interactions and noise. Particles move at a constant speed v on a two-dimensional space and, in a single step of the dynamics, each particle adopts the direction of motion of a randomly chosen neighboring particle within a distance R=1, with the addition of a perturbation of amplitude η (noise). We investigate how the global level of particles' alignment (order) is affected by their motion and the noise amplitude η. In the static case scenario v=0 where particles are fixed at the sites of a square lattice and interact with their first neighbors, we find that for any noise η>0 the system reaches a steady state of complete disorder in the thermodynamic limit, while for η=0 full order is eventually achieved for a system with any number of particles N. Therefore, the model displays a transition at zero noise when particles are static, and thus there are no ordered steady states for a finite noise (η>0). We show that the finite-size transition noise vanishes with N as η_{c}^{1D}∼N^{-1} and η_{c}^{2D}∼(NlnN)^{-1/2} in one- and two-dimensional lattices, respectively, which is linked to known results on the behavior of a type of noisy voter model for catalytic reactions. When particles are allowed to move in the space at a finite speed v>0, an ordered phase emerges, characterized by a fraction of particles moving in a similar direction. The system exhibits an order-disorder phase transition at a noise amplitude η_{c}>0 that is proportional to v, and that scales approximately as η_{c}∼v(-lnv)^{-1/2} for v≪1. These results show that the motion of particles is able to sustain a state of global order in a system with voter-like interactions.
我们研究了一个关于自驱动粒子集体行为的模型，该模型存在成对复制相互作用和噪声。粒子在二维空间中以恒定速度(v)移动，在动力学的单个步骤中，每个粒子采用距离(R = 1)内随机选择的相邻粒子的运动方向，并加上幅度为(\eta)（噪声）的扰动。我们研究粒子排列的全局水平（有序度）如何受到它们的运动和噪声幅度(\eta)的影响。在静态情况下，即(v = 0)时，粒子固定在正方形晶格的位置上并与其最近邻相互作用，我们发现对于任何噪声(\eta>0)，在热力学极限下系统会达到完全无序的稳态，而对于(\eta = 0)，对于任何粒子数(N)的系统最终都会达到完全有序。因此，当粒子静止时，该模型在零噪声处显示出转变，所以对于有限噪声（(\eta>0)）不存在有序稳态。我们表明，在一维和二维晶格中，有限尺寸转变噪声分别随着(N)消失，即(\eta_{c}^{1D}\sim N^{-1})和(\eta_{c}^{2D}\sim (N\ln N)^{-1/2})，这与催化反应中一类噪声选民模型行为的已知结果相关。当粒子被允许在空间中以有限速度(v>0)移动时，会出现一个有序相，其特征是一部分粒子沿相似方向移动。系统在噪声幅度(\eta_{c}>0)处表现出有序 - 无序相变，该幅度与(v)成正比，并且对于(v\ll1)，其比例近似为(\eta_{c}\sim v(-\ln v)^{-1/2})。这些结果表明，粒子的运动能够在具有类似选民相互作用的系统中维持全局有序状态。
