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Contributions of different parts of spin-spin interactions to quantum correlations in a spin ring model in an external magnetic field

We study quantum correlations in a bipartite heteronuclear $(N-1)\times1$ system in an external magnetic field. The system consists of a spin ring with an arbitrary number $N-1$ of spins on the ring and one spin in its center. The spins on the ring are connected by secular dipole-dipole interactions and interact with the central spin through the Heisenberg $zz$-interaction. We show that the quantum discord, describing quantum correlations between the ring and the central spin, can be obtained analytically for this model in the high temperature approximation. The model allows us to find contributions of different parts of the spin-spin interactions to quantum correlations. We also investigate the evolution of quantum and classical correlations at different numbers of spins.