The (111) surface of noble metals is usually treated as an isolated two dimensional (2D) triangular lattice completely decoupled from the bulk. However, unlike topological insulators, other bulk bands cross the Fermi level. We here introduce an effective tight-binding model that accurately reproduces results from first principles calculations, accounting for both surface and bulk states. We numerically solve the many-body problem of two quantum impurities sitting on the surface by means of the density matrix renormalization group. By performing simulations in a star geometry, we are able to study the non-perturbative problem in the thermodynamic limit with machine precision accuracy. We find that there is a non-trivial competition between Kondo and RKKY physics and as a consequence, ferromagnetism is never developed, except at short distances. The bulk introduces a variation in the period of the RKKY interactions, and therefore the problem departs considerably from the simpler 2D case. In addition, screening, and the magnitude of the effective indirect exchange is enhanced by the contributions from the bulk states.
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