论文标题
随机二聚体模型中激发的鲁棒性
Robustness of Excitations in the Random Dimer Model
论文作者
论文摘要
随机二聚体模型的基态解在此之后的临界点上，并以随机链接激发显示。在本文中，我们通过施加最大的重量激发来测试随机二聚体模型的鲁棒性对随机链接激发。我们从数值上计算模型中产生的曲线的缩放指数以及分形维度。尽管存在强大的尺寸校正，但结果与随机链接激发的结果兼容。此外，还研究了另一种激发的形式，即ε-耦合激发。我们发现，近乎最佳的配置属于与旅行推销员问题相同的普遍性类别。因此，我们证实了组合优化问题的缩放特性的猜想，这是针对二维晶格的最小重量匹配的特定情况。该文档是在2021年在伦敦国王学院的MSC复合系统建模课程中提交的。特别是，我要感谢我的主管Gabriele Sicuro博士的见解和指导。
The ground state solution of the random dimer model is at a critical point after, which has been shown with random link excitations. In this paper we test the robustness of the random dimer model to the random link excitation by imposing the maximum weight excitation. We numerically compute the scaling exponents of the curves arising in the model as well as the fractal dimension. Although strong finite size corrections are present, the results are compatible with that of the random link excitation. Furthermore, another form of excitation, the ε - coupling excitation is studied. We find that near-optimal configurations belong to the same universality class as the travelling salesman problem. Thus, we confirm a conjecture on the scaling properties of combinatorial optimisation problems, for the specific case of minimum weight perfect matchings on 2-dimensional lattices. This document was submitted as my thesis project for the MSc Complex Systems Modelling course at King's College London in 2021. In particular, I would like to thank my supervisor, Dr Gabriele Sicuro for his insights and guidance.
