electron Green’s function $\Im G_{p\s}(\iome)$ for $T=0.016$, $\d=0.05$ and increasing strength of external magnetic field. Data from QMC calculations. []{data-label="fig3.2"}](fig12.eps){width="45.00000%"}

Anti-ferromagnetic ordering {#sec4.2}
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At low temperature, we expect the development of anti-ferromagnetic (AFM) correlations a result of super-exchange between neighboring $f$-electrons assisted by the hybridization with $p$-orbital states. In this section we investigate the onset of an AFM long-range ordered state and its effect on the coherence scale using the extension of the DMFT equations to long-range order detailed in Appendix \[apx2\].

To begin with we report in the staggered magnetization $m_{AF}=
1/N\sum_i (-1)^{i} \bra n_{fi\up}-n_{fi\dw}\ket$ as a function of the temperature for various doping. The transition appears to be of second order in the whole doping region. The Néel temperature $T_N$, extracted from a power-law fit of the data, is maximum at zero doping and decreases by adding holes, as in the single-band Hubbard model. [^1]

The onset of an AFM ordering of the local $f$-moments reinstates the Fermi liquid properties in the tiny hole-doped regime. This effect is illustrated in the left panel of , where we present the evolution of the imaginary part of $\Sigma_{p\s}(\iome)$ from the paramagnetic NFL phase to the AFM ordered phase. The 