Alignment phase transition in socially driven motion.

Abstract

Collective fs 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 meters, 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 pseudopotential model that captures the transition as a nonequilibrium 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.