The interface between the plus and minus phases in the low temperature 3D Ising model has been intensely studied since Dobrushin’s pioneering works in the early 1970’s established its rigidity. Advances in the last five years yielded the tightness of the maximum of this interface, in a cylinder of side length $n$, around a mean that is asymptotically $c \log(n)$ for an explicit $c$ (depending on the temperature). In this talk we will present new analogous results for the 3D Potts models. Compared to 3D Ising, the Potts model and its lack of monotonicity form obstacles for existing methods, calling for new proof ideas, while its interfaces (and associated extrema) exhibit richer behavior.

Joint work with Joseph Chen.