We investigate spectral diffusion decay using a model for solids that consists of two-level-systems (TLSs) interacting via strain fields. For the case when the rate of TLS flips vanishes, we find algebraic decay of correlation functions of the local field. We show that properties of equilibrium fluctuations are in agreement with the hierarchical picture proposed by Basche and Moerner : TLSs far away produce fast fluctuations that are small in magnitude, and close TLSs produce large fluctuations that are less frequent.