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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.