Phase Transition of Hard Disk Systems with Vicsek-type Interactions

Abstract

The phase diagram of self-propelled hard disk systems with Vicsek-type alignment interactions was investigated by event-driven molecular dynamics simulations. The model incorporates two competing order parameters: the polar order-disorder transition associated with collective velocity alignment (Vicsek model) and the orientational order arising from solid-fluid transitions (Alder transition) induced by excluded volume effects. The incompressibility of hard disks suppresses motility-induced phase separation at high packing fractions. Distinctive fluctuations were observed near the transition point, accompanied by anomalous shifts in the transition point as functions of noise intensity and packing fraction. Analysis of local configurational parameters -- specifically, orientational order and circularity of free volume -- provides insight into the microscopic origins of these anomalous phase transition shifts.

Figures (4)

• Figure 1: (Color online) The polar order parameter $\psi$ as a function of noise $\eta$ in densely packed hard disk systems with $\nu=0.72$, for various values of the Vicsek interaction time interval $\Delta t^*$. The inset shows the packing fraction $\nu$ dependence of $\psi$ at a fixed $\Delta t^*=10$.
• Figure 2: (Color online) Contour map of the global orientational order parameter $\Phi_6^{\rm G}$ in the $\nu - \eta$ plane at $(N, \Delta t^* ) = (4096, 10)$. The snapshots color-coded by orientation direction $arg(\phi_6^i)$, at $\nu = 0.72$ for $\eta =0.1, 1.2\pi$, and $1.9\pi$ (from left to right)
• Figure 3: (Color online) The global orientational order parameter $\Phi_6^{\rm G}$ and local orientational order parameter $\Phi_6^{\rm L}$ as a function of $\eta$ for different $\Delta t^*$ and $N$ at a fixed packing fraction $\nu = 0.72$.
• Figure 4: (Color online) The probability distribution functions of the local circularity $c_i^*$ based on that of equilibrium are shown for each noise value $\eta$. The inset shows the total circularity $\@fontswitch\mathcal{C}$. The snapshots color-coded by $c_i^*$ and free volume shape (drawn in curves) at $\nu = 0.70$ for $\eta = 0.1\pi$ (A) and $1.9\pi$ (B).