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 Zd (d≥3) in its pure phases is proven to decay exponentially fast throughout the ordered regime (β>βc 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: (β,h)=(βc,0).