Fabio Martinelli , Enzo Olivieri 
Some Remarks on Pathologies of Renormalization Group Transformations for the Ising Model
(31K, plain TeX)

ABSTRACT.  The results recently obtained by van 
Enter, Fernandez 
and Sokal [EFS] on non-Gibbsianness of the measure
$\nu\,=\,T_b\,\mu_{\beta ,h}$ arising from the application
of a single decimation transformation $T_b$, with spacing 
$b$, to the 
Gibbs measure $\mu_{\beta ,h}$ of the Ising model, for 
suitably 
chosen large inverse temperature $\beta$ and non zero 
external field 
$h$, are critically analyzed. In particular we show that 
if, keeping 
fixed the same values of $\beta$, $h$ and $b$, one iterates 
a 
sufficiently large number of times $n$ the transfomation 
$T_b$, one 
obtains a new measure $\nu '\,=\,(T_b)^n\,\mu_{\beta 
,h}$ which is 
Gibbsian and moreover very weakly coupled.