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Updated references, small rewording, corrected typos

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent two-part exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion:

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work.