Graded cluster expansion for lattice systems

Details Graded cluster expansion for lattice systems Graded cluster expansion for lattice systems

2011-10-27

arxiv.org/abs/1110.6028v1

Communications in Mathematical Physics 258, 405-443, 2005

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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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