I will discuss how rigorous renormalization group methods can be used to construct a massless QFT over a space with hierarchical structure. The model under study is a phi-4 perturbation of a three dimensional fractional Gaussian Free Field and is meant to capture some of the behavior of the Wilson-Fisher 4-epsilon fixed point. Among our results is anomalous scaling for the composite field in this model. I will also show how methods from statistical mechanics can be used to prove the full scale invariance of this QFT. (Joint work with Abdelmalek Abdesselam and Gianluca Guadagni.)