A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories
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 \textit{K. Gawedzki} and \textit{A. Kupiainen} [Triviality of \(\Phi^ 4_ 4\) and all that in a hierarchy model approximation. J. Stat. Phys. 29, 683-699 (1982), and Rigorous renormalization group and asymptotic freedom. In: Scaling and self-similarity in physics (renormalization in statistical mechanics and dynamics), J. Fröhlich (ed.), Progress in Physics, Vol. 7: Birkhäuser (1983)]. 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.
critical lattice systems of unbounded spins
scientific article; zbMATH DE number 4068035
scientific article