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 ${\mathbb{Z}}^d$ ($d\ge 3$) 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 the model's phase diagram except for the critical point: $(\beta ,h)=({\beta }_c,0)$.

29 pages, 3 figures. A new corollary (the so-called ratio weak mixing property) has been added. The exposition has been modified based on the comments of the referee. Accepted for publication in the Communications in Mathematical Physics

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