- 03-47 L. Bertini, E.N.M. Cirillo, E. Olivieri
- A combinatorial proof of tree decay of semi-invariants
Feb 11, 03
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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