The dynamics-from-permutations of classical Ising spins is generalized here for an arbitrarily long chain. This serves as an ontological model with discrete dynamics generated by pairwise exchange interactions defining the unitary update operator. The model incorporates a finite signal velocity and resembles in many aspects a discrete free field theory. We deduce the corresponding Hamiltonian operator and show that it generates an exact terminating Baker-Campbell-Hausdorff formula. Motivation for this study is provided by the Cellular Automaton Interpretation of Quantum Mechanics. We find that our ontological model, which is classical and deterministic, appears as if of quantum mechanical kind in an appropriate formal description. However, it is striking that (in principle arbitrarily) small deformations of the model turn it into a genuine quantum theory. This supports the view that quantum mechanics stems from an epistemic approach handling physical phenomena.

中文翻译：

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量子自旋是本体论自旋的小扰动吗？

经典 Ising 自旋的排列动力学在这里被推广到任意长链。这是一个本体模型，具有由定义单一更新算子的成对交换交互生成的离散动态。该模型结合了有限信号速度，并在许多方面类似于离散自由场理论。我们推导出相应的哈密顿算子并证明它生成了精确的终止 Baker-Campbell-Hausdorff 公式。这项研究的动机是由量子力学的细胞自动机解释提供的。我们发现我们的本体论模型是经典的和确定性的，在适当的形式描述中看起来好像是量子力学类型的。然而，令人惊讶的是（原则上任意）模型的小变形将其变成了真正的量子理论。这支持了量子力学源于处理物理现象的认知方法的观点。