A classical local cellular automaton can describe an interacting quantum field theory for fermions. We construct a simple classical automaton for a particular version of the Thirring model with imaginary coupling. This interacting fermionic quantum field theory obeys a unitary time evolution and shows all properties of quantum mechanics. Classical cellular automata with probabilistic initial conditions admit a description in the formalism of quantum mechanics. Our model exhibits interesting features as spontaneous symmetry breaking or solitons. The same model can be formulated as a generalized Ising model. This euclidean lattice model can be investigated by standard techniques of statistical physics as Monte Carlo simulations. Our model is an example how quantum mechanics emerges from classical statistics.

经典的局部细胞自动机可以描述费米子的相互作用量子场理论。我们为虚构耦合的Thirring模型的特定版本构造了一个简单的经典自动机。这种相互作用的铁离子量子场论服从单一时间演化，并显示了量子力学的所有特性。具有概率初始条件的经典细胞自动机承认量子力学形式主义的描述。我们的模型表现出有趣的特征，例如自发对称破坏或孤子。可以将同一模型公式化为广义Ising模型。可以通过统计物理学的标准技术（如蒙特卡洛模拟）来研究该欧氏晶格模型。我们的模型是量子力学如何从经典统计中出现的一个例子。