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Graded cluster expansion for lattice systems

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arxiv 1110.6028 v1 pith:VYEOR57C submitted 2011-10-27 cond-mat.stat-mech

L. Bertini , Emilio N.M. Cirillo , E. Olivieri This is my paper · ORCID
classification cond-mat.stat-mech
keywords latticeclusterexpansionmixingsystemsapparentlyapplicationarising
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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