Three-dimensional motility-induced pinning transition

Investigate whether low diffusion produces a spontaneous motility-induced pinning transition in the three-dimensional active Potts model and determine whether the transition generates structurally richer jammed networks.

Background

The paper observes that low diffusion can drive spontaneous motility-induced pinning through kinetic trapping in two-dimensional active Potts systems. The three-dimensional model introduces additional spatial pathways and may therefore exhibit qualitatively different arrested structures.

The authors explicitly propose extending the analysis to three dimensions to determine whether motility-induced pinning occurs there and whether its jammed states have richer structure than their two-dimensional counterparts.

References

Several questions remain open. The critical size and density of a perturbing droplet could provide a quantitative measure of polar-liquid stability, while the formation, growth, lifetime, and survival probability of spontaneous droplets could further characterize metastability. The three-dimensional model also provides a framework for studying active systems in intrinsically three-dimensional environments. Since low diffusion can drive spontaneous motility-induced pinning (MIP) through kinetic trapping in two dimensions, an immediate extension would be to investigate this transition in three dimensions and determine whether it produces structurally richer jammed networks.

— Phase separation, morphology, and metastability in the three-dimensional active Potts model  (2609.37436 - Dutta et al., 29 Sep 2026) in Discussion section