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Dynamic phase transition in the contact process with spatial disorder: Griffiths phase and complex persistence exponents
Physical Review E ( IF 2.4 ) Pub Date : 2020-02-24 , DOI: 10.1103/physreve.101.022128
Priyanka D. Bhoyar , Prashant M. Gade

We present a model which displays the Griffiths phase, i.e., algebraic decay of density with continuously varying exponents in the absorbing phase. In the active phase, the memory of initial conditions is lost with continuously varying complex exponents in this model. This is a one-dimensional model where a fraction r of sites obey rules leading to the directed percolation class and the rest evolve according to rules leading to the compact directed percolation class. For infection probability ppc, the fraction of active sites ρ(t)=0 asymptotically. For p>pc, ρ()>0. At p=pc, ρ(t), the survival probability from a single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence Pl()>0 for ppc and Pl()=0 for p>pc. For pps, local persistence Pl(t) decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as p1. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increase with p. We note that the underlying lattice or disorder does not have a self-similar structure.

中文翻译:

空间无序接触过程中的动态相变:格里菲斯相和复杂的持久指数

我们提出了一个显示格里菲斯相的模型,即在吸收相中指数连续变化的密度的代数衰减。在活动阶段,此模型中连续变化的复杂指数会丢失初始条件的记忆。这是一维模型,其中分数[R的站点遵循导致定向渗滤类的规则,其余站点根据导致紧凑的定向渗滤类的规则进行演化。感染可能性ppC,活跃网站的比例 ρŤ=0渐近地 对于p>pC ρ>0。在p=pC ρŤ,单个种子的存活概率以及从单个种子对数衰减开始的平均活性位点数。当地的持久性P>0 对于 ppCP=0 对于 p>pC。对于pps,本地持久性 PŤ作为幂定律衰减,且指数不断变化。持久指数显然很复杂,因为p1个。复数指数表示持久性的对数周期性振荡。对数周期振荡的波长和幅度随p。我们注意到,潜在的晶格或无序不具有自相似的结构。
更新日期:2020-02-24
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