 94235 von Dreifus H., Klein A., Perez J. P.
 TAMING GRIFFITHS' SINGULARITIES: INFINITE DIFFERENTIABILITY OF QUENCHED
CORRELATION FUNCTIONS
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Jul 15, 94

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Abstract. We prove infinite differentiability of the magnetization and
of all quenched correlation functions for disordered spin systems
at high temperature or strong magnetic field in the presence of
Griffiths' singularities. We also show
uniqueness of the Gibbs state and exponential decay of truncated correlation
functions with probability one. Our results are obtained through new simple
modified high temperature or low activity expansions whose convergence can be
displayed by elementary probabilistic arguments. Our results require no
assumptions on the probability distributions of the random parameters,
except for the obvious one of no percolation of infinite couplings, and,
in the strong field situation, for the also obvious requirement that
zero magnetic fields do not percolate.
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