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.
Graded cluster expansion for lattice systems / BERTINI MALGARINI, Lorenzo; Cirillo, Emilio Nicola Maria; Enzo, Olivieri. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - STAMPA. - 258:2(2005), pp. 405-443. [10.1007/s00220-005-1360-3]
Graded cluster expansion for lattice systems
BERTINI MALGARINI, Lorenzo;CIRILLO, Emilio Nicola Maria;
2005
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
