We prove two inequalities for the direct and truncated correlation for the nearest-neighboor one-dimensional Edwards-Anderson model with symmetric quenched disorder. The second inequality has the opposite sign of the GKS inequality of type II. In the non symmetric case with positive average we show that while the direct correlation keeps its sign the truncated one changes sign when crossing a suitable line in the parameter space. That line separates the regions satisfying the GKS second inequality and the one proved here.
Griffiths inequalities and Gibbs-Bogoliubov inequality for general gauge glasses with Gaussian disorder on Nishimori line
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究院）；School of Computing, Institute of Science Tokyo（东京科学大学理工学院）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）；Research and Education Institute for Semiconductors and Informatics, Kumamoto University（熊本大学半导体与信息教研院）；Sigma-i Co., Ltd.（Sigma-i有限公司）
