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.

Methods
UWB-RFID Technology:

We used Ultra-Wideband Radio Frequency Identification (UWB-RFID) technology to continuously track children’s positions within the classroom. Each child wore a vest equipped with two UWB-RFID tags sewn near the left and right hips. These tags transmitted spatial data, including time, tag ID, and three-dimensional coordinates, at a frequency of 2-4 Hz to four receivers mounted at the corners of the classroom. This dual-tag configuration enabled high-resolution tracking of both position and orientation during natural preschool activities without disrupting classroom routines.

Studied Classrooms:

The study was conducted in preschool classrooms in Florida, over a four-year period from 2016 to 2020, involving multiple cohorts of children. Children wore RFID-equipped vests and participated in typical daily activities such as play, reading, painting, eating, and handwashing. Movements outside the classroom (e.g., bathroom trips) were excluded. Wearing the vests did not noticeably alter children's behavior. Classrooms were furnished with standard preschool furniture and varied in layout and size. Figure 2 in the main text provides a visual overview of the classroom environments, including 3D renderings, XY spatial layouts, and annotated floorplans for datasets LC1 and LC2.