- 04-207 L. Bertini, E.N.M. Cirillo, E. Olivieri
- Graded cluster expansion for lattice systems
Jul 9, 04
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Abstract. In this paper we develop a general theory which provides
a unified treatment of two apparently different problems.
The weak Gibbs property of measures arising from the application
of Renormalization Group maps and the mixing properties of
disordered lattice systems in the Griffiths' phase.
We suppose that the system satisfies a mixing condition
in a subset of the lattice whose complement is sparse enough
namely, large regions are widely separated.
We then show how it is possible to construct a convergent
multi-scale cluster expansion.