A Complex Topological Phase in C-Spin Active Matter

Abstract: This work introduces a new theoretical model for active matter ("complementary-spins" or c-spins), exploring the interplay of positional and orientational order in mobile agents with rotational freedom, divided into two populations with contrasting interactions. The system's behavior depends on its size and a control parameter (circular anisotropy) that splits the agents' natural rotational frequencies. Key findings include distinct phases based on anisotropy: Small Anisotropy: Stable, regular equilibrium patterns emerge. Moderate Anisotropy: Formation of complex, non-equilibrium topological point defects (vortex states), which are bistable with uniform patterns. These robust, self-repairing defects exhibit counter-rotating c-spin loop trains, spin-momentum locking, and dissipationless flow, classified by a two-valued topological charge. High Anisotropy: Transition to active turbulence and loss of order. Statistical analysis reveals a double phase transition at a critical value: a standard symmetry-breaking transition and a novel topological phase transition activating the vortex complexes. Increasing system size enhances organizational complexity and the development of spin-momentum locked transport networks. This model provides a new framework for understanding robustness and morphogenesis in living systems.