自旋玻璃基态对相互作用扰动的鲁棒性和稳定性
Robustness and Stability of Spin Glass Ground States to Perturbed Interactions
摘要：
在许多科学和工程学科中，重要的是考虑给定系统的输出由于输入的扰动而发生的变化。在这里，我们调查的玻璃相$\pm J$自旋玻璃在零温度下通过计算的基态的单一相互作用的符号翻转的鲁棒性。对于随机图和谢灵顿-柯克帕特里克模型，我们发现相对较大的债券配置，产生相同的基态。这些集合本身可以被分析为相互作用域的子图，我们计算它们的许多拓扑性质。特别是，我们发现，这些子图的鲁棒性，相当于平均度，是远远高于人们期望从随机模型。最值得注意的是，它与子图的大小以相同的对数方式缩放，如在RNA二级结构折叠、蛋白质四级结构、基因调控网络以及遗传编程模型的基因型-表型图中发现的那样。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。
英文摘要：
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.
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