Abstract
We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic ϕ4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2n-point functions are also given. A simple construction of the continuum ϕ quantum field theory (d<4), based on these inequalities, is described in a companion paper.
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