Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature

Abstract: The truncated two-point function of the ferromagnetic Ising model on $\mathbb Z<sup>d$ ($d\ge3$) in its pure phases is proven to decay exponentially fast throughout the ordered regime ($\beta&gt;\beta_c$ 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: $(\beta,h) = (\beta_c,0)$.