论文标题
经典随机图上结构平衡系统的热性能
Thermal properties of structurally balanced systems on classical random graphs
论文作者
论文摘要
在温度建模的影响下，社会关系的动态以及达到结构平衡状态（Heider平衡）的可能性，讨论了占据经典随机图的节点的相互作用的参与者。根据图密度$ d $，可以观察到从平衡到系统不平衡状态的平滑交叉或一阶相变，随着热噪声水平的提高。可以观察到一阶相变的最小图密度$ d_ \ text {min} $，随着系统尺寸$ n $作为$ d_ \ text {min} \ propto n^{ - 0.58（1）} $，可以观察到一阶相变的减小。对于图形密度，$ d> d_ \ text {min} $降低的临界温度$ t_c^\ star = t_c/t_c（d = 1）$随着图形密度作为$ t_c^\ star \ star \ propto d^{1.719（6）} $，独立于系统尺寸$ n $。
The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) under the influence of the temperature modeling the social noise level are discussed for interacting actors occupying nodes of classical random graphs. Depending on the graph density $D$, either a smooth cross-over or a first-order phase transition from a balanced to an imbalanced state of the system is observed with an increase of the thermal noise level. The minimal graph density $D_\text{min}$ for which the first-order phase transition can be observed decreases with system size $N$ as $D_\text{min}\propto N^{-0.58(1)}$. For graph densities $D>D_\text{min}$ the reduced critical temperature $T_c^\star=T_c/T_c(D=1)$ increases with the graph density as $T_c^\star\propto D^{1.719(6)}$ independently of the system size $N$.
