Rate of cluster decomposition via Fermat-Steiner point

In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories.