We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization group (SDRG) method, a phenomenological theory of rare regions, and numerical simulations. We find that, for interactions decaying as an inverse power of the distance, the persistence probability tends to a non-zero limit not only in the inactive phase but also in the critical point. Thus, unlike in the contact process with short-range interactions, the persistence in the limit $t\to\infty$ is a discontinuous function of the control parameter. For stretched exponentially decaying interactions, the limiting value of the persistence is found to remain continuous, similar to the model with short-range interactions.

中文翻译：

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具有长程相互作用的无序接触过程中的持久性不连续性

我们通过结合强无序重整化群 (SDRG) 方法、稀有区域的现象学理论和数值模拟，研究了在具有长程相互作用的无序接触过程中非平稳时间演化过程中的局部持续概率。我们发现，对于作为距离的反幂衰减的相互作用，持续概率不仅在非活动阶段而且在临界点趋向于非零极限。因此，与短程相互作用的接触过程不同，极限 $t\to\infty$ 中的持久性是控制参数的不连续函数。对于拉伸的指数衰减相互作用，发现持久性的极限值保持连续，类似于具有短程相互作用的模型。