元胞自动机的相变
Phase Transitions of Cellular Automata
AI总结：
本文系统探讨元胞自动机中的相变现象，涵盖密度相变、损伤扩散、异步诱导相变、混沌相变及拓扑影响，并介绍改进的平均场技术和唯象重整化群方法。
摘要：
我们探索元胞自动机中相变的若干方面。我们首先回顾离散系统（Ising模型）统计力学的标准表述，说明作为Markov链和随机过程的Monte Carlo方法。然后我们使用简单模型表述元胞自动机问题，并说明不同类型的可能相变：一阶和二阶密度相变、损伤扩散、确定性规则的稀释、异步诱导相变、同步现象、混沌相变以及拓扑的影响。我们说明了改进的平均场技术和唯象重整化群方法。
英文摘要：
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic processes. We then formulate the cellular automaton problem using simple models, and illustrate different types of possible phase transitions: density phase transitions of first and second order, damage spreading, dilution of deterministic rules, asynchronism-induced transitions, synchronization phenomena, chaotic phase transitions and the influence of the topology. We illustrate the improved mean-field techniques and the phenomenological renormalization group approach.
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