复杂网络上集群行为与自旋模型

复杂系统中的集群行为(collective behavior)是复杂系统涌现性的重要表现之一, 它通过微观个体之间的相互作用, 在宏观上表现出一定的时空或功能有序结构．已有研究表明, 个体之间相互作用的网络结构对复杂系统的集群行为有重要影响．基于复杂网络上的自旋模型, 介绍了复杂网络上的集群行为的部分研究进展． 首先简要介绍了自旋模型的相变现象以及网络结构对相变行为的影响; 其次, 介绍了以自旋模型为基础应用到社会经济等领域中的工作, 包括舆论形成、羊群效应以及分隔现象(segregation)等, 尤其关注网络结构对集群行为的影响, 最后介绍了基于自旋模型的网络社团划分方法．对进一步的发展方向进行了初步的讨论．

COLLECTIVE BEHAVIOR AND SPIN MODEL ON COMPLEX NETWORKS

Collective behaviors are important emergent phenomena in complex systems, from which macroscopic spatiotemporal or functional structure will emerge via interactions between microscopic individuals. Previous studies indicated that the structure of complex network related with the interaction between individuals had important effects on collective behaviors in complex systems. Based on the researches on Ising model of complex networks, recent studies on collective behaviors on complex networks are reviewed in this article. First, the critical phenomena emerged in Ising model is presented as well as the effects of network's structure on phase transition. Second, efforts are focused on the application of Ising model to social and economic systems, including opinion formation, herd behavior and segregation phenomenon, with emphasis laid on the effects of network's structure on collective behaviors. Thirdly, the approaches to detect community structure of networks based on Ising model are presented, and finally discussions and concluding remarks are given.