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.

A combinatorial proof of tree decay of semi-invariants / BERTINI MALGARINI, Lorenzo; Cirillo, Emilio Nicola Maria; Enzo, Olivieri. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 115:1-2(2004), pp. 395-413. [10.1023/b:joss.0000019813.58778.bf]

A combinatorial proof of tree decay of semi-invariants

BERTINI MALGARINI, Lorenzo;CIRILLO, Emilio Nicola Maria;
2004

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/237389
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