  Magnetic materials are typically described in terms of the Heisenberg model,
which provides an accurate account of thermodynamic properties when combined
with first principles calculations. This approach is usually based on an energy
mapping between density functional theory and a classical Heisenberg model.
However, for two-dimensional systems the eigenenergies of the Heisenberg model
may differ significantly from the classical approximation, which leads to
modified expressions for exchange parameters. Here we demonstrate that density
functional theory yields local magnetic moments that are in accordance with
strongly correlated anti-ferromagnetic eigenstates of the Heisenberg
Hamiltonian. This implies that density functional theory provides a description
of these states that conforms with the quantum mechanical eigenstates of the
model. We then provide expressions for exchange parameters based on a proper
eigenstate mapping to the Heisenberg model and find that they are typically
reduced by 10 % compared to a classical analysis. Finally, we calculate the
corrections to critical temperature for magnetic ordering for a previously
predicted set of two-dimensional ferromagnetic insulators and find that the
inclusion of quantum effects may reduce the predictions of critical
temperatures by up to 7 %.
