稀释和加密三角剖分上结构平衡系统的热性质
Thermal properties of structurally balanced systems on diluted and densified triangulations
摘要：
社会关系的动态和达到结构平衡状态（海德平衡）的可能性进行了讨论的各种网络的相互作用的影响下的温度建模的社会噪音水平。为此，考虑两种主要类型的晶格。第一个是通过从规则三角形晶格中删除一些链接来创建的，以产生稀释的三角形晶格，第二个是通过添加更多的链接来创建增强的三角形晶格。在这两种情况下，可能的图密度的全部范围进行了讨论，由少数分离的三元组和完全连接的网络组成的网络的极端情况下的限制。结果表明，如果平均节点度太接近于表征正三角格的值，则平衡状态的存在是不可能的。否则，根据温度，平衡（或部分平衡）和不平衡状态都是可能的。然而，仅对于足够密集的图，观察到第一种相变，而较少增强的网络（和所有稀释）表明两种状态之间的平滑交叉。的交叉温度是大小无关的，仅为稀释的三角形晶格，并取决于系统的大小为增强的三角形晶格，也是这种情况下观察到的相变的临界温度在更密集的增强晶格。
英文摘要：
The dynamics of social relations and the possibility of reaching the state of structural balance (Heider balance) are discussed for various networks of interacting actors under the influence of the temperature modeling the social noise level. For that purpose, two main types of lattices are considered. The first is created by removing some links from a regular triangular lattice to produce a diluted triangular lattice, and the second by adding more links to create an enhanced triangular lattice. In both those cases, the full range of possible graph densities is discussed, limited by the extreme cases of networks which consist of a small number of separated triads and fully connected networks. It is shown that the existence of the balanced state is not possible if the average node degree is too close to the value characterizing the regular triangular lattice. Otherwise, both balanced (or partially balanced) and imbalanced states are possible, depending on the temperature. However, only for graphs which are dense enough a phase transition of the first kind is observed, while less enhanced networks (and all diluted) indicate a smooth cross-over between the two states. The cross-over temperatures are size-independent only for the diluted triangular lattices and depend on the size of the system for the enhanced triangular lattices, as is the case also for the critical temperatures of the phase transition observed in denser enhanced lattices.
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