标题： 两色网络中的自发对称性破缺与相共存 显示英文标题

标题： Spontaneous Symmetry Breaking and Phase Coexistence in Two-Color Networks

摘要： 我们考虑了一个平衡系综，其中包含具有固定顶点度数的大型Erdős-Renyi拓扑随机网络，包含两种类型的顶点，黑色和白色，以键连接概率$p$随机准备。 网络能量是所有同色三元组（要么是黑色要么是白色）的总和，权重为三元组的化学势，$\mu$。 通过最小化系统能量，我们看到对于某些正的$\mu$，形成两个主要的同色簇，由一个“弦”状的$N_{bw}$个黑白键连接。 我们证明了系统表现出临界行为，在$N_{bw}(\mu)$-曲线上的广泛平台出现，这与一阶相变中的spinodal分解有关。 从弦理论的角度来看，平台的形成可以解释为二维引力中婴儿宇宙之间的纠缠。 我们推测，观察到的经典现象可以视为量子色动力学中手征凝聚形成的玩具模型。 显示英文摘要

摘要： We have considered an equilibrium ensemble of large Erd\H{o}s-Renyi topological random networks with fixed vertex degree and two types of vertices, black and white, prepared randomly with the bond connection probability, $p$. The network energy is a sum of all unicolor triples (either black or white), weighted with chemical potential of triples, $\mu$. Minimizing the system energy, we see for some positive $\mu$ formation of two predominantly unicolor clusters, linked by a "string" of $N_{bw}$ black-white bonds. We have demonstrated that the system exhibits critical behavior manifested in emergence of a wide plateau on the $N_{bw}(\mu)$-curve, which is relevant to a spinodal decomposition in 1st order phase transitions. In terms of a string theory, the plateau formation can be interpreted as an entanglement between baby-universes in 2D gravity. We have conjectured that observed classical phenomenon can be considered as a toy model for the chiral condensate formation in quantum chromodynamics.