标题： 一种拓扑玻璃 显示英文标题

标题： A Topological Glass

摘要： 我们提出并研究了一个具有玻璃行为的模型。 该模型的状态空间由所有具有$n$个节点的球面三角剖分组成，其中一半是红色节点，另一半是蓝色节点。 红色节点希望有5个邻居，而蓝色节点希望有7个。 不同邻居数的节点的能量被假定为正值。 动力学过程是翻转两个相邻三角形的对角线，概率取决于温度。 我们证明了这个系统趋于一个稳态，且趋于过程是指数级缓慢的，并证明了稳态是无序的。 我们还研究了局部能量景观，并证明其具有自旋玻璃中已知的层次结构。 最后，我们证明了演化可以描述为一种稀薄气体，具有粒子的自发生成和湮灭碰撞。 显示英文摘要

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.