Non-local Potts model on random lattice and chromatic number of a plane
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 ) interact. We study the vacuum states of this model and present the results of numerical simulations and discuss qualitative features of the corresponding patterns. Conjectured relation with the chromatic number of a plane problem is discussed.
Cite
@article{arxiv.2107.08508,
title = {Non-local Potts model on random lattice and chromatic number of a plane},
author = {V. Shevchenko and A. Tanashkin},
journal= {arXiv preprint arXiv:2107.08508},
year = {2026}
}
Comments
18 pages, 11 figures, accepted version, sections on comparison of algorithms and checking of model stability are added, new references are added