Before revision:  We establish that if the interpolation method is valid for a family of graphs satisfying the self-reducibility property, then this family exhibits a form of correlation decay property which is asymptotic Strong Spatial Mixing (SSM) at distances \omega(\log ^{3 n), where n is the number of nodes of the graph.
After revision:  We establish that if the interpolation method is valid for a family of graphs satisfying the self-reducibility property, then this family exhibits a form of correlation decay property which is asymptotic Strong Spatial Mixing (SSM) at distances \omega(\log n), where n is the number of nodes of the graph.