We derive a Kirkwood-Salzburg integral equation, with positive defined kernel, for the states of lattice models of statistical mechanics and quantum field theory. The equation is defined in the thermodynamic limit, and its iterative solution is convergent; moreover, positivity leads to an exact a priori bound on the iteration. The equation's relevance as a reliable algorithm for lattice calculations is therefore suggested, and it is illustrated with a simple application. It should provide a viable alternative to Monte Carlo methods for models of statistical mechanics and lattice gauge theories.
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