AI 中文总结
本研究在带不同核函数的随机几何图团渗流中，发现了含幂律行为的格里菲斯相，明确其边界特征并分析幂律、指数核下的行为，为相关领域提供了研究基础。
AI 中文摘要
本研究探讨了具有不同核函数（用于量化几何约束）的随机几何图系综中的团渗流问题。对于锐截止情况，我们发现了具有幂律行为的宽扩展临界格里菲斯相。格里菲斯相的一个边界是ER系综渗流临界点的推广，对应于大而有限团内出现渗流的情况；第二个边界对应于整个聚类系统中渗流变得可行的参数空间点。对于幂律核，我们识别出更丰富的行为，即有效ER区域与几何区域之间存在依赖于团大小的边界，且该情况下格里菲斯相依然存在。最后，我们分析了指数核的情况，并简要讨论了研究结果的潜在应用。
英文摘要
In this study, we discuss the clique percolation in the ensembles of random geometric graphs with different kernels that quantify the geometrical constraints. For the sharp cut-off we find the wide Griffiths phase of extended criticality with the power-law behavior. One boundary of the Griffiths phase is the generalization of a percolation critical point for the ER ensemble when the percolation within the large but finite cluster emerges. The second boundary corresponds to the point in the parameter space when the percolation in the entire clustered system becomes available. For the power-law kernel, richer behavior with a clique-size-dependent boundary between the effective ER and geometric regimes has been identified. The Griffiths phase in this case exists as well. Finally, the pattern with the exponential kernel has been analyzed. We briefly discuss the possible applications of our findings.
