Pattern formation and phase transition in the collective dynamics of a binary mixture of polar self-propelled particles

The collective behavior of a binary mixture of polar self-propelled particles (SPPs) with different motile properties is studied. The binary mixture consists of slow-moving SPPs (sSPPs) of fixed velocity $v_s$ and fast-moving SPPs (fSPPs) of fixed velocity $v_f$. These SPPs interact via a short-range interaction irrespective of their types. They move following certain position and velocity update rules similar to the Vicsek model (VM) under the influence of an external noise $\eta$. The system is studied at different values of $v_f$ keeping $v_s=0.01$ constant for a fixed density $\rho=0.5$. Different phase-separated collective patterns that appear in the system over a wide range of noise $\eta$ are characterized. The fSPPs and the sSPPs are found to be orientationally phase-synchronized at the steady-state. We studied an orientational order-disorder transition varying the angular noise $\eta$ and identified the critical noise $\eta_c$ for different $v_f$. Interestingly, both the species exhibit continuous transition for $v_f<100v_s$, and discontinuous transition for $v_f>100v_s$. A new set of critical exponents is determined for the continuous transitions. However, the binary model is found to be non-universal as the values of the critical exponents depend on the velocity. The effect of interaction radius on the system behavior is also studied.