Correlation Inequalities for Spin Glass in one Dimension

We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched dis-order. The second inequality has the opposite sign of the GKS inequality of typeII. In the non symmetric case with positive average we show that while the directcorrelation keeps its sign the truncated one changes sign when crossing a suitableline in the parameter space. That line separates the regions satisfying the GKSsecond inequality and the one proved here.