Mapping the total energies obtained from first principles calculations to model Hamiltonians is a powerful technique to explore the magnetic ground state of a system. We analyze the applicability of this approach in the presence of highly polarizable substrates, e.g. for an ultrathin Fe layer on Pd(111), Rh(111), Ru(0001), or Tc(0001). We find that the traditionally accepted model Hamiltonians (Heisenberg plus nearest neighbor higher-order spin Hamiltonians) are not sufficient to capture the magnetic interactions in these systems and examine new terms that can be included to improve the description. Challenges for this technique are exemplified by the double-rowwise antiferromagnetic (AFM) ground state predicted for Fe/Rh(111). Usually, magnetic structures are explained within classical spin models like the Heisenberg model, H ¼ Àð1=2ÞTheir foundation results primarily from quantum mechanical exchange interactions of different orders and between different neighbors, and is expressed by spin operators, Ŝ. Typically, the operator is then replaced by the expectation value, S, and quantum fluctuations are neglected. The change from FM to AFM order of the Fe monolayers deposited on Ag(001) or W(001)