00-367 Christof Kuelske
On the Gibbsian nature of the random field Kac model under block-averaging (253K, Postscript) Sep 18, 00
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Abstract. We consider the Kac-Ising model in an arbitrary configuration of local magnetic fields $\eta=(\eta_i)_{i\in \Z^d}$, in any dimension $d$, at any inverse temperature. We investigate the Gibbs properties of the `renormalized' infinite volume measures obtained by block averaging any of the Gibbs-measures corresponding to fixed $\eta$, with block-length small enough compared to the range of the Kac-interaction. We show that these measures are Gibbs measures for the same renormalized interaction potential. This potential depends locally on the field configuration $\eta$ and decays exponentially, uniformly in $\eta$, for which we give explicit bounds.

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