L. Bertini, E.N.M. Cirillo, E. Olivieri
A combinatorial proof of tree decay of semi-invariants
(325K, Postscript)

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.