论文标题
在随机图上的零温度ISING模型中的订单disorder转变
Order-disorder transition in the zero-temperature Ising model on random graphs
论文作者
论文摘要
已知零温度的ISING模型在足够致密的随机图中达到完全有序的基态。在稀疏的随机图中，动力学在接近零的磁化时被无序的局部最小值吸收。在这里，我们发现有序状态和无序状态之间的非平衡过渡的平均程度会随着图形大小而缓慢生长。该系统显示出双重性：在达到的吸收状态下绝对磁化的分布是双峰的，峰值仅为零和统一。对于固定的系统大小，吸收的平均时间与平均程度的函数非单向行为。平均吸收时间的峰值随着系统大小的功率定律而增长。这些发现与网络上的社区发现，意见动态和游戏相关。
The zero-temperature Ising model is known to reach a fully ordered ground state in sufficiently dense random graphs. In sparse random graphs, the dynamics gets absorbed in disordered local minima at magnetization close to zero. Here, we find that the non-equilibrium transition between the ordered and the disordered regime occurs at an average degree that slowly grows with the graph size. The system shows bistability: The distribution of the absolute magnetization in the reached absorbing state is bimodal, with peaks only at zero and unity. For a fixed system size, the average time to absorption behaves nonmonotonically as a function of average degree. The peak value of the average absorption time grows as a power law of the system size. These findings have relevance for community detection, opinion dynamics, and games on networks.
