Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Science. 2013 Mar 8;339(6124):1185-7. doi: 10.1126/science.1230813.
When dynamics in a system proceeds under suppressive external bias, the system can undergo an abrupt phase transition, as can happen when an epidemic spreads. Recently, an explosive percolation (EP) model was introduced to understand such phenomena. The order of the EP transition has not been clarified in a unified framework covering low-dimensional systems and the mean-field limit. We introduce a stochastic model in which a rule for dynamics is designed to avoid the formation of a spanning cluster through competitive selection in Euclidean space. We use heuristic arguments to show that in the thermodynamic limit and depending on a control parameter, the EP transition can be either continuous or discontinuous if d < d(c) and is always continuous if d ≥ d(c), where d(c) is the spatial dimension and d is the upper critical dimension.
当系统中的动力学在抑制性外部偏置下进行时，系统可能会发生突然的相变，就像传染病传播时可能发生的情况一样。最近，引入了一种爆炸渗流（EP）模型来理解这种现象。在涵盖低维系统和平均场极限的统一框架中，尚未阐明 EP 相变的顺序。我们引入了一个随机模型，其中设计了一种动力学规则，通过在欧几里得空间中的竞争选择来避免形成跨越簇。我们使用启发式论证来表明，在热力学极限下并且取决于控制参数，如果 d < d(c)，则 EP 相变可以是连续的或不连续的，如果 d ≥ d(c)，则 EP 相变总是连续的，其中 d(c)是空间维度，d 是上临界维度。
