main results of this work, namely the strongly incoherent nature of the low temperature metallic state. A phase-diagram of the model is presented at the end of this section. In we study the magnetic properties of the model. Finally, we present a magnetic phase-diagram of the model which illustrates how magnetic competition helps stabilizing the incoherent behavior at low temperature.

Model and theoretical framework {#sec1}
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The Periodic Anderson Model {#sec1.1}
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The periodic Anderson model describes a set of non-dispersive strongly correlated electrons, locally hybridizing with a band of conduction electrons. The model Hamiltonian is written in the following form: The operators $p_{i\s}$ ($p_{i\s}^+$) destroy (create) conduction band electrons with hopping amplitude $t_{ij}$ and energy $\ep0$. The operators $f_{i\s}$ ($f_{i\s}^+$) destroy (create) electrons in the non-dispersive orbital with energy $\ed0$. The terms proportional to $\tpd$ describe the hybridization between the two species. The interaction term $H_I$ describes the strong on-site Coulomb repulsion experienced by $f$-orbital electrons.

The non-interacting lattice Green’s function reads: with $\epsk$ the dispersion of the conduction electrons: $\epsk=
\sum_{<ij>}e^{-i\ka\cdot(\mathbf{r}_i-\mathbf{r}_j)}\, t_{ij}$. The corresponding interacting Green’s function can be expressed by means of the following matrix Dyson equation: where is the self-energy matrix $\hat{\Sigma}_\s$. The non-interacting nature of 