Aug 2 – 6, 2021
Europe/Brussels timezone

Nonlocal Potts model on random lattice and chromatic number of the plane

Aug 5, 2021, 10:30 AM


Parallel contribution Focus Subsection: Emergent Gauge Fields and Chiral Fermions Parallels Focus Subsection


Aleksei Tanashkin (Far Eastern Federal University)


Statistical models are a powerful tool for investigation of complex system's behaviour. Most of the models considered in the literature are defined on regular lattices with nearest neighbour interactions. The models with nonlocal interaction kernels have been less studied. In our study we investigate an example of such a model - the nonlocal $q$-color Potts model on a random $d=2$ lattice. Only same color spins at unit distance (within some margin $\delta$) interact. The goal is to find minimum energy configuration starting from some random coloring of the sites. We present the results of supercomputer simulations of this system and discuss the corresponding patterns. Conjectured relation with the problem of finding the chromatic number of the plane is discussed.

Primary authors

Vladimir Shevchenko (NRC Kurchatov Institute) Aleksei Tanashkin (Far Eastern Federal University)

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