The random-walk representation of classical spin systems and correlation inequalities - II. The skeleton inequalities

We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic φ{symbol}⁴ 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 2 n-point functions are also given. A simple construction of the continuum φ{symbol}_d⁴ quantum field theory (d<4), based on these inequalities, is described in a companion paper.