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A combinatorial proof of tree decay of semi-invariants

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arxiv 1110.6034 v1 pith:QEUXNCPE 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 combinatorialdecayprooftreeanalyticityargumentsfieldsgibbs
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We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi--invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions. This hypothesis holds for completely analytical Gibbs fields; in this context the tree decay of semi--invariants has been proven via analyticity arguments. However the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so called Griffiths' phase when analyticity arguments fail.

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