  In this note we prove a correlation inequality for local variables of a Gibbs
field based on the connectivity by active hyperbonds in a random cluster
representation of the non overlap configuration distribution of two independent
copies of the field. As a consequence, we show that absence of
Machta-Newman-Stein blue bonds percolation implies uniqueness of Gibbs
distribution in EA Spin Glasses. In dimension two this could constitute a step
towards a proof that the critical temperature is zero.
