A rigorous block spin approach to massless lattice theories

The renormalization group technique is used to study rigorously the lambda(nabla phi)4 perturbation of the massless lattice field phi in dimensions d >= 2. Asymptoticity pf the perturbation expansion in powers of lambda is established for the free energy density. This is achieved by using Kadanoff's block spin transformation successively to integrate out high momentum degrees of freedom and by applying ideas previously used by Gallavotti and Balaban in the context of the ultraviolet problems. The method works for arbitrary semibounded polynomials in nabla v and Δ phi. (orig.)