Fig. 4: Susceptibility and finite-size scaling.
From: Formation of stable and responsive collective states in suspensions of active colloids
a Experimental probability distribution of the rotational order parameter |OR| for different values of Δ showing a continuous transition between a swarm (black) and a swirl (green) of a group of N = 50 APs. b Corresponding susceptibility χ as a function of the deviation angle Δ (symbols). Error bars correspond to the standard deviation obtained from different measurements. Lines correspond to simulations where DR,sim is identical (dashed) and three times larger (solid) compared with the experimental value DR,exp = 0.0028 s−1. c χ vs. Δ obtained from simulations for different particle numbers N = [50, 100, 150, 250, 500] and DR,sim = 3DR,exp. d Corresponding rescaled susceptibility \(\widetilde \chi = \chi \cdot N^{ - \gamma /\nu }\) vs. the rescaled deviation angle \(\widetilde {\mathrm{\Delta}} = \frac{{\Delta} \, - \, {\Delta}_{c}}{{\Delta}_{c}} \cdot N^{1/\nu}\). The critical exponents ν, γ and the value of Δc were used as free fitting parameters. The best data collapse is achieved for ν = 3.87, γ = 2.24 and Δc = 56.15°. e \(\left\langle {\left| {O_{\mathrm{R}}} \right|} \right\rangle\) vs. Δ for simulations with N = [50, 100, 150, 250, 500]. f Corresponding rescaled order parameter \(\widetilde {\left\langle {\left| {O_{\mathrm{R}}} \right|} \right\rangle } = \left\langle {\left| {O_{\mathrm{R}}} \right|} \right\rangle \cdot N^{\beta /\nu }\) vs. \({\tilde{\mathrm{\Delta }}}\) with β as a free fitting parameter (ν and Δc were taken from d). Best collapse is achieved for β = 0.66. Symbols in d and f show experimental data for N = 50 and N = 120.
