It is known that the Ising model on at a given temperature is a finitary factor of an i.i.d. process if and only if the temperature is at least the critical temperature. Below the critical temperature, the plus and minus states of the Ising model are distinct and differ from one another by a global flip of the spins. We show that it is only this global information which poses an obstruction to being finitary by showing that the gradient of the Ising model is a finitary factor of i.i.d. at all temperatures. As a consequence, we deduce a volume-order large deviation estimate for the energy. Results in the same spirit are shown for the Potts model, the so-called beach model, and the six-vertex model. We also introduce a coupling between the six-vertex model with and a new Edwards–Sokal type graphical representation of it, which we believe is of independent interest.

中文翻译：

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梯度模型的有限编码和六顶点模型的新图形表示

众所周知，当且仅当温度至少为临界温度时，在给定温度下的 Ising 模型是独立同分布过程的有限因子。在临界温度以下，伊辛模型的正负状态是不同的，并且通过自旋的全局翻转而彼此不同。我们通过表明 Ising 模型的梯度在所有温度下都是独立同分布的有限因子，表明只有这种全局信息才会阻碍有限性。因此，我们推导出能量的体积阶大偏差估计。Potts 模型、所谓的海滩模型和六顶点模型显示了相同的结果。我们还引入了六顶点模型与以及它的新 Edwards-Sokal 类型图形表示，我们认为它具有独立的兴趣。