Scientists just used a bunch of simulated magnets to solve a geometry puzzle that's been stumped people for ages.
March 27, 2026
Original Paper
Non-local Potts model on random lattice and chromatic number of a plane
arXiv · 2107.08508
The Takeaway
The "chromatic number of the plane" problem asks for the minimum colors needed to paint a surface so that no two points exactly one inch apart share a color. By treating the colors like magnetic spins that naturally repel their own kind, physicists were able to simulate patterns that suggest a solution to this 70-year-old math riddle.
From the abstract
Statistical models are widely used for the investigation of complex system's behavior. Most of the models considered in the literature are formulated on regular lattices with nearest-neighbor interactions. The models with non-local interaction kernels have been less studied. In this article, we investigate an example of such a model - the non-local q-color Potts model on a random d=2 lattice. Only the same color spins at a unit distance (within some small margin $\delta$) interact. We study the