Some examples of quenched self-averaging in models with Gaussian disorder

In this paper we give an elementary approach to several results of Chatterjee in (Disorder chaos and multiple valleys in spin glasses (2013) arXiv:0907.3381, Comm. Math. Phys. 337 (2015) 93-102), as well as some generalizations. First, we prove quenched disorder chaos for the bond overlap in the Edwards-Anderson type models with Gaussian disorder. The proof extends to systems at different temperatures and covers a number of other models, such as the mixed p-spin model, Sherrington-Kirkpatrick model with multi-dimensional spins and diluted p-spin model. Next, we adapt the same idea to prove quenched self-averaging of the bond magnetization for one system and use it to show quenched self-averaging of the site overlap for random field models with positively correlated spins. Finally, we show self-averaging for certain modifications of the random field itself.