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摘要翻译：
我们提出并研究了一个具有玻璃态行为的模型。该模型的状态空间是由一个具有$n$节点的球面的所有三角剖分给出的，其中一半是红的，一半是蓝的。红色节点希望有5个邻居，而蓝色节点希望有7个邻居。具有不同邻居数目的节点的能量应该是正的。该动力学是以温度依赖的概率翻转两个相邻三角形的对角线。我们证明了该系统有一个指数缓慢的稳态，并证明了该稳态是无序的。我们还研究了局域能量景观，并表明它具有自旋玻璃中已知的层次结构。最后，我们证明了粒子的演化可以描述为稀薄气体的演化，稀薄气体具有自发产生的粒子和湮没碰撞。
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英文标题：
《A Topological Glass》
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作者：
Jean-Pierre Eckmann
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics 物理学
二级分类：Chaotic Dynamics 混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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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.
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PDF链接：
https://arxiv.org/pdf/704.0976
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