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.