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Exponential decay of truncated correlations for the Ising model in any dimension for all but the critical temperature
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abstract
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: $(\beta,h) = (\beta_c,0)$.
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Finitary codings for gradient models and a new graphical representation for the six-vertex model
Gradient fields of low-temperature spin models (Ising, Potts, beach, six-vertex) are finitary factors of i.i.d. processes even when the models themselves are not.
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