论文标题
与空间障碍的接触过程中的动态相变：Griffths阶段和复杂的持久指数
Dynamic Phase Transition in the Contact Process with Spatial Disorder: Griffths Phase and Complex Persistence Exponents
论文作者
论文摘要
我们提出了一个模型，该模型显示Griffith阶段，即密度的代数衰减，并在吸收阶段不断变化。在主动阶段，在此模型中，由于连续变化的复杂指数而丢失了初始条件的记忆。这是1-D模型，其中站点的分数r遵守导致渗透类（DP）类的规则，其余的根据导致紧凑的定向渗透（CDP）类进化。对于感染概率$ p <p_c $，活动站点的分数$ρ（t）= 0 $渐近。对于$ p> p_c $，$ρ（infty）> 0 $。在$ p = p_c $，$ρ（t）$，单个种子的生存概率和单个种子衰变从对数中开始的活跃站点的平均数量。 $ p <p_c $和$ p_l（\ infty）= 0 $ for $ p> p_c $的本地持久性$ p_l（\ infty）> 0 $ for $ p <p_c $和$ p_l（\ infty）= 0 $。对于$ p> p_s $，本地持久性$ p_l（t）$衰减为具有不断变化的指数的电源法。持久性指数显然很复杂，因为$ p \ rightarrow 1 $。复杂的指数暗示对数持久性周期性振荡。对数周期性振荡的波长和幅度随p而增加。我们注意到，潜在的晶格或混乱没有自相似的结构。
We present a model which displays Griffiths phase i.e. algebraic decay of density with continuously varying exponent in the absorbing phase. In active phase, the memory of initial conditions is lost with continuously varying complex exponent in this model. This is 1-D model where fraction r of sites obey rules leading to directed percolation (DP) class and the rest evolve according to rules leading to compact directed percolation (CDP) class. For infection probability $p < p_c$, the fraction of active sites $ρ(t) = 0$ asymptotically. For $p > p_c$, $ρ(infty) > 0$. At $p = p_c$, $ρ(t)$, the survival probability from single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence $P_l(\infty) > 0$ for $p < p_c$ and $P_l(\infty) = 0$ for $p > p_c$. For $p > p_s$, local persistence $P_l(t)$ decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as $p\rightarrow 1$. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increases with p. We note that underlying lattice or disorder does not have self-similar structure.
