社会经济动力学作为共同进化网络上的可解自旋系统
Socio-economical dynamics as a solvable spin system on co-evolving networks
摘要：
我们认为社会系统中的代理人不仅具有其国家的特点，但也有自由选择他们的互动伙伴，以最大限度地提高他们的效用。我们将这样的系统映射到一个伊辛模型中，自旋动态耦合的动态网络中的链接。在这个模型中，有两个动力学量在正则框架中朝向最小能量状态排列：自旋s_i和邻接矩阵元素c_{ij}。该模型是完全可解的，因为微正则配分函数作为c_{ij}最小化能量的直接结果减少到二项式因子的乘积。我们解决了系统的有限尺寸和两个可能的热力学极限，并讨论了相图。
英文摘要：
We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantities which arrange towards a minimum energy state in the canonical framework: the spins, s_i, and the adjacency matrix elements, c_{ij}. The model is exactly solvable because microcanonical partition functions reduce to products of binomial factors as a direct consequence of the c_{ij} minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discuss the phase diagrams.
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