K-Mers渗流中的临界现象

Scaling Behaviors of K-Mers Percolation

摘要: 本文旨在深入研究k-mers渗流模型的标度行为与普适性特性，揭示其在统计物理中临界现象的内在规律。采用蒙特卡洛模拟方法，以每个模型下的最大的五个gap为样本，通过有限尺度分析对数据进行处理，计算了不同k值(k = 1~9)下的临界指数和临界点，并探讨其标度行为。研究发现，计算的临界指数完全一致，这表明k-mers渗流模型临界行为的普适性。此外，通过调节参数因子，使得这些概率分布图能够统一标度，从而进一步验证了普适性质。这些发现表明，在不同参数条件下，渗流模型表现出高度一致的临界行为，揭示了其内在的统一性。这一发现不仅为统计物理中临界现象的理解提供了新的理论依据，还为该模型在复杂系统中的应用奠定了基础。

Abstract: This study aims to investigate scaling behavior and universality class of the k-mers percolation model, revealing the critical phenomena within statistical physics. Using Monte Carle simulation method, the five-largest gaps were sampled and conducted finite-size scaling analysis. We calculated the critical exponents and critical points for various k values (k = 1~9), as well as its universal scaling form. Our findings indicate the universality class of the critical behaviors for k-mers percolation model. Moreover, by adjusting a parameter, observe that data from various gaps and system volumes collapse well, further validating the universality. These results suggest this percolation model exhibits highly consistent critical behavior. This discovery not only provides a new theoretical basis for understanding critical phenomena in statistical physics but also a foundation for the application of this model in more complex systems.