Exact Inequality for Random Systems: Application to Random Fields

An inequality relating averages of generalized correlations to averages of generalized susceptibilities for Gaussian field distributions is presented. This inequality is applied to random-field systems to prove under the assumption of a continuous transition the (tree level) decoupling of the quenched two-point function. By assumption of only a power-law divergence, a lower bound for $\eta$ is obtained. It rules out the possibility that some recent experimental and numerical results reflect equilibrium properties near a continuous transition.