- 04-208 L. Bertini, E.N.M. Cirillo, E. Olivieri
- Renormalization Group in the uniqueness region: weak Gibbsianity and convergence.
Jul 9, 04
(auto. generated ps),
of related papers
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.