A messy layer of matter appearing during a phase transition behaves exactly like two random paths that never touch.
April 24, 2026
Original Paper
Discontinuous transition in 2D Potts: II. Order-Order Interface convergence
arXiv · 2604.21669
The Takeaway
The interface between ordered phases in a 2D Potts model collapses into a precise geometric pattern during a phase transition. A disordered layer emerges at the transition point, bounded by lines that behave like non-intersecting Brownian motions. This specific structure only appears during this discontinuous transition and vanishes in other regimes. Researchers proved that these boundaries converge to a very specific mathematical curve as the system size increases. Understanding this middle ground between phases helps explain how materials like magnets or alloys suddenly change their properties under heat.
From the abstract
The $q$-state Potts model is an archetypical model for various types of phase transitions. We consider it on the square grid and focus on the regime where it undergoes a discontinuous transition, that is $q>4$. At the transition point $T_c(q)$, there are exactly $q+1$ extremal Gibbs measures (pure phases): $q$ ordered (monochromatic) and one disordered (free). This work establishes for the first time the wetting phenomenon in a precise geometric form and in the entire regime of discontinuity $q>