Open questions about multi-band Hubbard models

There is an interesting review article
Magnetism and its microscopic origin in iron-based high-temperature superconductors
by Pengcheng Dai, Jiangping Hu, Elbio Dagotto

The authors highlight

• the diversity of materials and types of magnetic order in the parent compounds 
• just giving a theoretical description of the parent compounds is a challenge
• that these materials are in an intermediate coupling (moderately? correlated) regime where weak-coupling treatments are inadequate 
• there are local magnetic moments at room temperature, which is well above most of the magnetic ordering temperatures
• how poorly understood the multi-band Hubbard model is, even at half filling

The phase diagram below is based on Hartree-Fock theory (which surely is quite inadequate). J_H is the Hund's rule coupling. The "physical region" is probably the parameter regime of the pnictides.

I am interested to know how this diagram compares to DMFT (dynamical mean-field theory) and DMRG studies on ladders.