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A recent rank 4 tensor field model generating 4D simplicial manifolds hasbeen proved to be renormalizable at all orders of perturbation theory[arXiv:1111.4997 [hep-th]]. The model is built out of $\phi^6$($\phi^6_{(1/2)}$), $\phi^4$ ($\phi^4_{(1)}$) interactions and an anomalousterm ($\phi^4_{(2)}$). The $\beta$-functions of this model are evaluated at twoand four loops. We find that the model is asymptotically free in the UV forboth the main $\phi^6_{(1/2)}$ interactions whereas it is safe in the$\phi^4_{(1)}$ sector. The remaining anomalous term turns out to possess aLandau ghost.

Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories