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