论文标题
无序接触过程中局部持久性的缩放
Scaling of local persistence in the disordered contact process
论文作者
论文摘要
我们研究了$ d = 1,2 $和$ 3 $尺寸的无序接触过程中局部持久性概率的时间依赖性。我们提出了一种使用强disorder重新归一化组（SDRG）技术来计算持久性的方法，然后我们在分析中以$ d = 1 $分析地将其应用于临界点，并以$ d = 2,3 $进行数值。根据结果，平均持久性在较晚的时间衰减，这是时间对数的逆力，具有通用，依赖于维度的广义指数。对于$ d = 1 $，显示出样本依赖性局部持久性的分布，其特征是有效持久指数的通用极限分布。通过在活动阶段稀有区域效应的现象学方法，我们获得了$ d = 1 $的平均持久性的非宇宙代数衰变，并增强了$ d> 1 $的功率定律。例外，对于随机稀释的晶格，代数衰减对$ d> 1 $有效，这是通过悬挂端的贡献来解释的。蒙特卡洛模拟证实了平均持久性时间依赖性的结果。我们还证明了持久性与回报概率的等效性，这是参数的宝贵工具。
We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dependent local persistences is shown to be characterized by a universal limit distribution of effective persistence exponents. By a phenomenological approach of rare-region effects in the active phase, we obtain a non-universal algebraic decay of the average persistence for $d=1$, and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay holds to be valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time-dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.
