Alignment Phase Transition in Socially Driven Motion (2506.01550v1)

Abstract: Collective human movement is a haLLMark of complex systems, exhibiting emergent order across diverse settings, from pedestrian flows to biological collectives. In high-speed scenarios, alignment interactions ensure efficient flow and navigation. In contrast, alignment in low-speed, socially engaged contexts emerges not from locomotion goals but from interpersonal interaction. Using high-resolution spatial and orientation data from preschool classrooms, we uncover a sharp, distance-dependent transition in pairwise alignment patterns that reflects a spontaneous symmetry breaking between distinct behavioral phases. Below a critical threshold of approximately 0.65\,m, individuals predominantly align side-by-side; beyond this range, face-to-face orientations prevail. We show that this transition arises from a distance-dependent competition among three alignment mechanisms: parallelization, opposition, and reciprocation, whose interplay generates a bifurcation structure in the effective interaction potential. A Fourier-based decomposition of empirical orientation distributions reveals these mechanisms, enabling the construction of a minimal pseudo-potential model that captures the alignment transition as a non-equilibrium phase transition. Monte Carlo simulations using the inferred interaction terms closely reproduce the empirical patterns. These findings establish a quantitative framework for social alignment in low-speed human motion, extending active matter theory to a previously unexplored regime of socially mediated orientation dynamics, with implications for modeling coordination and control in biological collectives and artificial swarms.