Field-controlled interfacial transport and pinning in an active spin system

Abstract

Field control provides a practical route to programmable active matter, yet how weak fields modify non-equilibrium coexistence and interfaces remains unclear. To address this, we study a minimal flocking model of active Potts particles coupled to an external field and show that even weak fields can reconfigure phase behavior and interfacial dynamics. For a homogeneous unidirectional field, the flocking phase is reshaped: the coexistence regime between an apolar gas and a polar liquid is replaced by a phase separation between two field-aligned polar phases: a low-density, weakly polarized background and a high-density, strongly polarized band, both moving along the field. When the system forms a dense longitudinal lane oriented transverse to the field, it executes a slow treadmilling motion against the field, driven by the weakly polarized background. If the system is divided into regions with opposite field directions, particles accumulate at the interface, leading to field-induced interface pinning with flocks performing back-and-forth oscillatory motion. In the presence of quenched random field orientations, this pinning favors a disordered state in which global order diminishes with increasing system size, consistent with Imry-Ma arguments, while the quenched disorder smoothens sharp first-order signatures, in line with the Aizenman-Wehr theorem, with activity modifying the scaling. A coarse-grained hydrodynamic theory supports these observations and is consistent with microscopic simulations.

Figures (9)

• Figure 1: (Color online) Steady-state features of 4-state APM under a homogeneous unidirectional field. (a--b) Steady-state snapshots for increasing $h$ and (a) $\epsilon=0.9$ and (b) $\epsilon=2.7$, exhibiting a phase separation at intermediate $h$ values. Black arrows indicate the motion direction of the particles. Color code: red ($\sigma=1$), green ($\sigma=2$), blue ($\sigma=3$), and black ($\sigma=4$). (c) Mean-square displacement for varying $h$ and $\epsilon=0.9$. (d--e) Time-averaged density and magnetization profiles, respectively, for $\beta=0.7$, $\epsilon=0.9$, and increasing $h$. Parameters: $D=1$, $\beta=0.5$, $\rho_0=3$, $L=512$. (f) $T-h$ phase diagram for $D=1$, $\epsilon=0.9$, and $\rho_0=3$. (g) $\epsilon-h$ phase diagram for $D=1$, $\beta=0.5$, and $\rho_0=3$. (h) $D-h$ state diagram for $\epsilon=2.7$, $\beta=1$, and $\rho_0=5$. The represented states are: polar liquid (dark-red up triangle), stripe (green circle), short-range order (blue square), and motility-induced pinning (orange down triangle).
• Figure 2: (Color online) Treadmilling of the longitudinal lane under a transverse field. (a) Steady-state snapshot starting from a lane of state $\sigma=2$ (black arrow) for a low field strength ($h=0.1$). The lane slowly moves in the opposite direction (blue arrow) of the field (red arrow). Color code: red ($\sigma=1$), green ($\sigma=2$), blue ($\sigma=3$), and black ($\sigma=4$). (b) Corresponding time-averaged density and magnetization profiles for state $\sigma=1$ and $\sigma=2$. The density profile is slightly tilted opposite to the field orientation. (c) Steady-state snapshot starting from a lane of state $\sigma=2$ for a higher field strength ($h=0.2$), showing a reorientation of the lane along the field. (d) Treadmilling velocity $v_{\rm tm}$ and maximum magnetization of the background $m_1/\rho$ as a function of the field strength $h$. $v_{\rm tm}$ reaches a plateau for large $h$ while the magnetization behaves almost linearly. Parameters: $D=1$, $\beta=0.7$, $\epsilon=2.7$, $\rho_0=4$, and $L=512$. Treadmilling velocity $v_{\rm tm}$ as a function of the field strength $h$ for: (e) $\beta=0.7$, $\rho_0=4$, and varying $\epsilon$; and (f) $\epsilon=2.7$, $\rho_0=\rho_*(\beta)$, and varying $\beta$.
• Figure 3: (Color online) Steady-state features of 4-state APM under a bidirectional field. (a-b) Steady state snapshot for $\epsilon=1.8$ and increasing $h$, exhibiting the bidirectional flocking and the field-induced interface pinning (FIIP) states, respectively. Color code: red ($\sigma=1$), green ($\sigma=2$), blue ($\sigma=3$), and black ($\sigma=4$). (c) Corresponding time-averaged density profiles for $\epsilon=1.8$ and varying $h$. (d) $\epsilon-h$ state diagram. Parameters: $D=1$, $\beta=1$, $\rho_0=4$, $L=1024$.
• Figure 4: (Color online) Steady-state features of 4-state APM under a random orientational field. (a--b) Steady-state snapshots for increasing $h$ and (a) $\epsilon=0.9$ and (b) $\epsilon=2.7$, starting from an ordered state. Color code: red ($\sigma=1$), green ($\sigma=2$), blue ($\sigma=3$), and black ($\sigma=4$). (c) Mean-square displacement for varying $h$ and $\epsilon=0.9$. (d) Global magnetization $\langle m \rangle$ as a function of $h$ for several $\epsilon$ and $L=64$. (e) Global magnetization $\langle m \rangle$ as a function of $L$ for several $\epsilon$ and $h=0.5$. Parameters: $D=1$, $\beta=1$, $\rho_0=3$, $L=512$. (f) Time-averaged density profiles for $\beta=0.7$, $\epsilon=0.9$, and increasing $h$. (g) $T-h$ phase diagram for $D=1$, $\epsilon=0.9$, and $\rho_0=3$. (h) $\epsilon-h$ phase diagram for $D=1$, $\beta=1$, and $\rho_0=3$.
• Figure 5: (Color online) Hydrodynamic theory under a homogeneous unidirectional field. (a--b) Steady state density and magnetization profiles for $\beta=0.55$, $\epsilon=0.9$, $\rho_0=3$, $L=512$, and increasing $h$. (c) $T-h$ phase diagram for $\rho_0=3$ and $\epsilon=0.9$. (d) $\epsilon-h$ phase diagram for $\rho_0=3$ and $\beta=0.5$. (e) Steady-state density and magnetization profiles for state $\sigma=1$ and $\sigma=2$. The density profile is slightly tilted opposite to the field orientation. (f) Treadmilling velocity $v_{\rm tm}$ and maximum magnetization of the background $m_1/\rho$ as a function of the field strength $h$. $v_{\rm tm}$ reaches a plateau for large $h$ while the magnetization behaves almost linearly. Parameters: $\beta=0.75$, $\epsilon=2.7$, $\rho_0=1.5$, and $L=512$. (g) Treadmilling velocity $v_{\rm tm}$ for varying $\epsilon$ for $\beta=0.75$ and $\rho_0=1.5$. (h) Treadmilling velocity $v_{\rm tm}$ for varying $\beta$ for $\epsilon=2.7$ and $\rho_0=\rho_*(\beta)$.