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A rigorous method is developed to handle the “large field problems” in the Wilson-Kadanoff renormalization group approach to critical lattice systems of unbounded spins. We use this method to study in a hierarchical approximation the non-Gaussian renormalization group fixed point which governs the infrared behaviour of critical lattice field theories in three dimensions. The method is an improvement of the analyticity techniques of Gawedzki and Kupiainen: using Borel summation techniques we are able to incorporate the “large field region” into the “perturbative region” so that the theory is completely described in terms of convergent expansions.

A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories