FZ Jülich, Jülich, Germany.
Phys Rev Lett. 2011 Jun 3;106(22):225701. doi: 10.1103/PhysRevLett.106.225701. Epub 2011 May 31.
We study four Achlioptas-type processes with "explosive" percolation transitions. All transitions are clearly continuous, but their finite size scaling functions are not entirely holomorphic. The distributions of the order parameter, i.e., the relative size s(max)/N of the largest cluster, are double humped. But-in contrast to first-order phase transitions-the distance between the two peaks decreases with system size N as N(-η) with η>0. We find different positive values of β (defined via (s(max)/N)∼(p-p(c))β for infinite systems) for each model, showing that they are all in different universality classes. In contrast, the exponent Θ (defined such that observables are homogeneous functions of (p-p(c))N(Θ)) is close to-or even equal to-1/2 for all models.
我们研究了四个具有“爆炸”渗流相变的 Achlioptas 型过程。所有的相变都是明显连续的，但它们的有限大小标度函数并不完全是全纯的。序参量（即最大簇的相对大小 s(max)/N）的分布是双重驼峰的。但是-与一级相变不同-两个峰值之间的距离随着系统大小 N 的增加而减小，呈 N(-η)的关系，其中 η>0。我们发现每个模型的β值（通过对于无限系统的 (s(max)/N)∼(p-p(c))β 定义）都不同，表明它们都属于不同的通用类。相比之下，对于所有模型，指数 Θ（定义为观测值是 (p-p(c))N(Θ)的齐次函数）接近甚至等于-1/2。
