Alignment phase transition in socially driven motion

Collective human movement is a hallmark of complex systems, exhibiting
emergent order across contexts from pedestrian flows to biological
collectives. In high-speed, directional settings, alignment ensures
efficient navigation, whereas in low-speed, undirectional, socially
engaged contexts, alignment arises from interpersonal interaction rather
than locomotion goals. Using high-resolution spatial and orientation data
from preschool classrooms, we uncover a sharp distance-dependent
transition in pairwise alignment that reflects a spontaneous symmetry
breaking between behavioral phases: below a threshold of ∼ 0.65 m,
side-by-side orientations dominate, while face-to-face orientations
prevail at larger distances. This transition stems from a
distance-dependent competition among three alignment mechanisms:
parallelization, opposition, and reciprocation, whose interplay generates
a bifurcation structure in the effective interaction potential. Fourier
decomposition of orientation distributions reveals these mechanisms,
enabling a minimal pseudo-potential model that captures the transition as
a non-equilibrium phase change. Monte Carlo simulations using inferred
interaction terms reproduce empirical patterns, establishing a
quantitative framework for social alignment with implications for
biological collectives and artificial swarms.