论文标题
自旋玻璃基态稳健性和稳定性与扰动相互作用
Robustness and Stability of Spin Glass Ground States to Perturbed Interactions
论文作者
论文摘要
在许多科学和工程学科中，重要的是要考虑由于输入的扰动而导致给定系统的输出发生了多少变化。在这里，我们通过计算单个相互作用的迹象的基态稳健性来调查零温度下的$ \ pm j $旋转眼镜的玻璃相。对于随机图和Sherrington-Kirkpatrick模型，我们发现了相对较大的键合配置集，它们会生成相同的基态。这些集合本身可以分析为相互作用域的子图，我们计算了许多拓扑特性。特别是，我们发现这些子图的鲁棒性（相当于平均程度）远高于一个随机模型的预期。最值得注意的是，它以相同的对数方式与子图的大小相同，与基因型 - 表型图中的大小相同，用于RNA二级结构折叠，蛋白质季季结构，基因调节网络以及用于基因程序的模型。这些不同系统之间的相似性表明，这种缩放可能具有更普遍的起源。
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero temperature by calculating the robustness of the ground states to flips in the sign of single interactions. For random graphs and the Sherrington-Kirkpatrick model, we find relatively large sets of bond configurations that generate the same ground state. These sets can themselves be analyzed as subgraphs of the interaction domain, and we compute many of their topological properties. In particular, we find that the robustness, equivalent to the average degree, of these subgraphs is much higher than one would expect from a random model. Most notably, it scales in the same logarithmic way with the size of the subgraph as has been found in genotype-phenotype maps for RNA secondary structure folding, protein quaternary structure, gene regulatory networks, as well as for models for genetic programming. The similarity between these disparate systems suggests that this scaling may have a more universal origin.
