Bounds on the decay of correlations for lambda ( nabla phi )/sup 4/ models

The author considers models, with an abelian continuous group of symmetry of the type: /b H/= Sigma /sub x/[/sup 1///sub 2 /( nabla /sub x/ phi )/sup 2/+/sup lambda ///sub 4 /( nabla /sub x/ phi )/sup 4/]. He generalizes Brascamp-Lieb inequalities to get ( lambda -independent) bounds on the low momentum behaviour of general correlation functions when these are truncated into two clusters. He then uses this result to derive an asymptotic expansion (up the second order in lambda ) of the dielectric constant of this system.