Local Analyticity and Bounds on the Truncated Correlation Functions in Disordered Systems

G. Gielis, C. Maes

1995, v.1, №4, 459-472

ABSTRACT

We consider Gibbs fields with local and unbounded random interactions in the regime of Griffiths' singularities. We prove that the singularities are not worse than that of the randomly diluted ferromagnet and obtain upper bounds $(\sim C^k(k!)^2)$ for the semi-invariants of order $k$, for high enough temperature. To obtain this result, we extend the notion of complete analyticity to that of local analyticity for non-translation invariant systems.

Keywords: Griffiths' singularities,spin glasses,semi-invariants,local analyticity