Figure 2

Cluster size as a function of U₀ for two different values of the density: green and blue for N = 10³, 2 × 10³, respectively, at fixed L. Other parameters as in Fig. 1. Continuous lines are obtained by linear numerical fits. In the ABP case (Panel (a)) we plot the diameter, d, of the ring cluster, while the AOUP case (Panel (b)) we show 2σ. In the AOUP case the label U₀ is a short-cut for \(\sqrt{2{D}_{a}/\tau }\). The appearance of configurations which exchange particles among clusters is indicated by violet symbols. Blue shades denote the occurrence of unstable clusters in the case N = 2 × 10³, while the same analysis for N = 10³ is not shown for the sake of clarity. The left vertical dashed line indicates the smallest value of the active force which displays the instability of at least one cluster in the steady state. The right vertical dashed line shows the beginning of the disordered phase. In panel (c) we show the radial probability density, ρ(r). Red diamonds refer to ABP, yellow triangles to AOUP. Black lines are the result of a numerical fit. In panel (d) we plot the pair correlation function, g(r), for different values of the active force both for ABP and AOUP dynamics, as shown in the legend.