生命起源模型中的非平衡相变
Nonequilibrium phase transitions in a model for the origin of life
摘要：
在无限扩散或平均场极限下，通过解析方法和在位置固定或接触过程极限下的蒙特卡罗模拟，研究了二维晶格中自复制分子小群体的持久性.分子由双全环复制子A模拟，该复制子A能够以生产率s通过二元裂变A + E -2A复制以及以速率c通过催化辅助复制2A + E -3A复制。此外，分子可以以速率$γ$降解成其源材料E。在渐近状态下，种群的特征可以由晶格中复制子的存在（活跃相）和不存在（空相）来描述。在这两个扩散制度中，我们发现，对于小的值的比率c/ $γ$这些阶段被分离的二阶相变，这是在普遍性类的定向渗流，而对于小的值s/ $gamma$的相变是一阶的。此外，我们说明了适用的动态蒙特卡罗方法，这是基于分析的几个活跃的细胞在一个无限的空晶格的中心，以解决出现的复制的问题的传播行为。而令人惊讶的是，我们表明，这种方法允许一个明确的非平衡相变的顺序识别。
英文摘要：
The requisites for the persistence of small colonies of self-replicating molecules living in a two-dimensional lattice are investigated analytically in the infinite diffusion or mean-field limit and through Monte Carlo simulations in the position-fixed or contact process limit. The molecules are modeled by hipercyclic replicators A which are capable of replicating via binary fission A + E --2A with production rates s as well as via catalytically assisted replication 2A + E --3A with rate c. In addition, a molecule can degrade into its source materials E with rate $γ$. In the asymptotic regime the population can be characterized by the presence (active phase) and the absence (empty phase) of replicators in the lattice. In both diffusion regimes, we find that for small values of the ratio c/$γ$ these phases are separated by a second-order phase transition which is in the universality class of the directed percolation, while for small values s/$gamma$ the phase transition is of first order. Furthermore, we illustrate the suitability of the dynamic Monte Carlo method, which is based on the analysis of the spreading behaviour of a few active cells in the center of an otherwise infinite empty lattice, to adress the problem of emergence of replicators. Rather surprisingly, we show that this method allows an unambiguous identification of the order of the nonequilibrium phase transition.
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