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 $\mathbb Z^d$($d\ge3$) 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 the model’s phase diagram except for the critical point: $(\beta ,h)=({\beta }_c,0)$.