无序与长距离扩散相互作用下接触过程中的密度平滑消失
Smoothly vanishing density in the contact process by an interplay of disorder and long-distance dispersal
AI总结：
本文通过蒙特卡洛模拟和数值重整化群研究接触过程在无序与长距离扩散共同作用下的相变行为，发现全局密度以无限级相变方式平滑消失，而局部持续性表现出混合级相变的不连续性。
摘要：
对生态种群动态的现实建模需要空间显式描述，这种描述能够考虑空间异质性以及长距离扩散。在此，我们针对一维和二维系统中同时存在这些因素的范式模型——接触过程，给出了蒙特卡洛模拟和数值重整化群结果。我们的结果证实了我们的解析论证，即密度在灭绝阈值处平滑地消失，其方式具有无限级相变的特征。全局密度这种极其平滑的消失意味着种群暴露于灭绝事件的程度增强。同时，一个反向序参量，即局部持续性，表现出混合级相变所特有的不连续性，因为它以代数方式趋近一个非普适临界值，指数为 $β_p'<1$。
英文摘要：
Realistic modeling of ecological population dynamics requires spatially explicit descriptions that can take into account spatial heterogeneity as well as long-distance dispersal. Here, we present Monte Carlo simulations and numerical renormalization group results for the paradigmatic model, the contact process, in the combined presence of these factors in both one and two-dimensional systems. Our results confirm our analytic arguments stating that the density vanishes smoothly at the extinction threshold, in a way characteristic of infinite-order transitions. This extremely smooth vanishing of the global density entails an enhanced exposure of the population to extinction events. At the same time, a reverse order parameter, the local persistence displays a discontinuity characteristic of mixed-order transitions, as it approaches a non-universal critical value algebraically with an exponent $β_p'<1$.
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