Discontinuous transition in 2D Potts: II. Order-Order Interface convergence

Moritz Dober; Alexander Glazman; Sébastien Ott

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arXiv · 2604.21669

Discontinuous transition in 2D Potts: II. Order-Order Interface convergence

Moritz Dober·Alexander Glazman·Sébastien Ott

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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 $q>4$: at $T_c(q)$, between two ordered phases a disordered layer emerges and, in the diffusive scaling, its boundaries converge to a pair of Brownian motions conditioned not to intersect. This is starkly different from the subcritical ($T 4$.

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Moritz Dober, Alexander Glazman, Sébastien Ott. 2026-04-23. Discontinuous transition in 2D Potts: II. Order-Order Interface convergence. https://arxiv.org/abs/2604.21669

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