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arXiv · 1506.00625

The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature

Michael Aizenman·Hugo Duminil-Copin
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Abstract

The truncated two-point function of the nearest-neighbor ferromagnetic Ising model on $\mathbb Z^d$ ($d\ge3$) in its pure phases is proven to decays exponentially fast throughout the ordered regime ($T<T_c$). Together with known results, this implies that the exponential clustering property holds throughout the model's phase diagram except for the critical point: $(T,h) = (T_c,0)$.

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Michael Aizenman, Hugo Duminil-Copin. 2015-06-01. The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature. https://arxiv.org/abs/1506.00625

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