Christof Kuelske
On the Gibbsian nature of the 
random field Kac model under block-averaging
(253K, Postscript)

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.