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.