摘要翻译：
考虑复杂演化网络中的铁磁大q$状态Potts模型，该模型等价于一个最优合作问题，其中Agent试图优化对合作收益和独立项目支持的总和。研究发现，这些智能体通常分为两类：一小部分$M$(Potts模型的磁化）属于一个大的合作簇，而其他的则是单独的一个人的项目。严格证明了齐次模型具有强烈的一级相变，对于随机相互作用（利益），该相变转向二级相变，并在Barab\'asi-Albert网络上对其性质进行了数值研究。有限尺寸过渡点的分布特征为移位指数$1/\tilde{\nu}'=.26(1)$和不同的宽度指数$1/\nu'=.18(1)$,而过渡点的磁化强度与网络的大小成比例$n$:$m\sim n^{-x}$，$x=.66(1)$。
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英文标题：
《Rounding of first-order phase transitions and optimal cooperation in
  scale-free networks》
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作者：
M. Karsai, J-Ch. Angl\`es d'Auriac, F. Igl\'oi
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Physics and Society        物理学与社会
分类描述：Structure, dynamics and collective behavior of societies and groups (human or otherwise). Quantitative analysis of social networks and other complex networks. Physics and engineering of infrastructure and systems of broad societal impact (e.g., energy grids, transportation networks).
社会和团体（人类或其他）的结构、动态和集体行为。社会网络和其他复杂网络的定量分析。具有广泛社会影响的基础设施和系统（如能源网、运输网络）的物理和工程。
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英文摘要：
  We consider the ferromagnetic large-$q$ state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: a fraction of $m$ (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barab\'asi-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, $1/\tilde{\nu}'=.26(1)$, and by a different width exponent, $1/\nu'=.18(1)$, whereas the magnetization at the transition point scales with the size of the network, $N$, as: $m\sim N^{-x}$, with $x=.66(1)$.
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PDF链接：
https://arxiv.org/pdf/704.1538