- 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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