拓扑玻璃
A Topological Glass
摘要：
提出并研究了一个具有玻璃态行为的模型。该模型的状态空间由具有$n$节点的球体的所有三角剖分给出，其中一半为红色，一半为蓝色。红色节点希望有5个邻居，而蓝色节点希望有7个邻居。具有不同数目邻居的节点的能量被假定为正。动力学是翻转两个相邻三角形的对角线，具有温度依赖的概率。我们表明，该系统有一个方法的稳定状态是指数缓慢，并表明，定态是无序的。我们还研究了当地的能源景观，并表明，它具有从自旋玻璃已知的层次结构。最后，我们表明，演化可以描述为一个自发产生的粒子和湮灭碰撞的稀薄气体。
英文摘要：
We propose and study a model with glassy behavior. The state space of the model is given by all triangulations of a sphere with $n$ nodes, half of which are red and half are blue. Red nodes want to have 5 neighbors while blue ones want 7. Energies of nodes with different numbers of neighbors are supposed to be positive. The dynamics is that of flipping the diagonal of two adjacent triangles, with a temperature dependent probability. We show that this system has an approach to a steady state which is exponentially slow, and show that the stationary state is unordered. We also study the local energy landscape and show that it has the hierarchical structure known from spin glasses. Finally, we show that the evolution can be described as that of a rarefied gas with spontaneous generation of particles and annihilating collisions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
