Exponential Decay of Truncated Correlations for the Ising Model in any Dimension for all but the Critical Temperature

The truncated two-point function of the ferromagnetic Ising model on ${\mathbb {Z}}^d$ ($d\ge 3$) in its pure phases is proven to decay exponentially fast throughout the ordered regime ($\beta >\beta _c$ and $h=0$). Together with the previously known results, this implies that the exponential clustering property holds throughout t...More