L. Bertini, E.N.M. Cirillo, E. Olivieri
Renormalization Group in the uniqueness region: weak Gibbsianity and convergence.
(897K, Postscript)

ABSTRACT.  We analyze the block averaging transformation applied to lattice gas 
models with short range interaction in the uniqueness region below 
the critical temperature. 
%We discuss the 
%Gibbs property of the renormalized measure and the convergence of 
%renormalized potential under iteration of the map. 
We prove weak Gibbsianity of the 
renormalized measure and convergence of the renormalized 
potential in a weak sense. 
Since we are arbitrarily close to the coexistence region we have a 
diverging characteristic length of the system: the correlation length or the 
critical length for metastability, or both. Thus, to perturbatively treat 
the problem we have to use a scale--adapted expansion. Moreover, such a model 
below the critical temperature resembles a disordered system in presence of 
Griffiths' singularity. Then the 
cluster expansion that we use must be graded with its minimal scale length 
diverging when the coexistence line is approached.