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We study the competition between Kondo physics and indirect exchange on monolayer black phos-phorous using a realistic description of the band structure in combination with the density matrixrenormalization group (DMRG) method. The Hamiltonian is reduced to a one-dimensional problemvia an exact canonical transformation that makes it amenable to DMRG calculations, yielding exactresults that fully incorporate the many-body physics. We find that a perturbative description of theproblem is not appropriate and cannot account for the slow decay of the correlations and the completelack of ferromagnetism. In addition, at some particular distances, the impurities decouple formingtheir own independent Kondo states. This can be predicted from the nodes of the Lindhard function.Our results indicate a possible route toward realizing dilute anti-ferromagnetism in phosphorene. Received: 19 September 2017, Accepted: 12 October 2017; Edited by: K. Hallberg; DOI: http://dx.doi.org/10.4279/PIP.090008 Cite as: A Allerdt, A E Feiguin, Papers in Physics 9, 090008 (2017)