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.
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.