Abstract
Statistical models are widely used for 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 interactions have been less studied. We investigate in the present article an example of such a model — non-local q-color Potts model on a random d=2 lattice, where only the same color spins at unit distance (within some small margin δ) interact. We analyze numerically the structure of the vacuum states in this model and discuss qualitative features of the corresponding patterns. Conjectured relation with the chromatic number of a plane problem is discussed.
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