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.

Bertini, L., Cirillo, E., Olivieri, E. (2004). A combinatorial proof of tree decay of semi-invariants. JOURNAL OF STATISTICAL PHYSICS, 115(1-2), 395-413 [10.1023/B:JOSS.0000019813.58778.bf].

A combinatorial proof of tree decay of semi-invariants

OLIVIERI, ENZO
2004-01-01

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.
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - Fisica Matematica
English
Cluster expansion; Disordered systems; Gibbs fields; Semi-invariants
Bertini, L., Cirillo, E., Olivieri, E. (2004). A combinatorial proof of tree decay of semi-invariants. JOURNAL OF STATISTICAL PHYSICS, 115(1-2), 395-413 [10.1023/B:JOSS.0000019813.58778.bf].
Bertini, L; Cirillo, E; Olivieri, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/30631
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