TAMING GRIFFITHS SINGULARITIES - INFINITE DIFFERENTIABILITY OF QUENCHED CORRELATION-FUNCTIONS

We prove infinite differentiability of the magnetization and of all qu enched correlation functions for disordered spin systems at high tempe rature or strong magnetic field in the presence of Griffiths' singular ities. We also show uniqueness of the Gibbs state and exponential deca y of truncated correlation functions with probability one. Our results are obtained through new simple modified high temperature or low acti vity expansions whose convergence can be displayed by elementary proba bilistic arguments. Our results require no assumptions on the probabil ity distributions of the random parameters, except for the obvious one of no percolation of infinite couplings, and, in the strong field sit uation, for the also obvious requirement that zero magnetic fields do not percolate.