复杂系统中的合作行为
Cooperative behaviour in complex systems
摘要：
在我的博士论文中，我使用统计和计算物理的方法研究了复杂系统中出现的合作现象。我的工作的目的也是研究相互作用的多体系统在其相变的临界行为，并通过分析和数值计算来描述它们的普遍特征。为了做到这一点，我完成了四个不同科目的学习。我的第一个研究课题是加权无标度网络中的非平衡相变。我研究的第二个问题是铁磁随机键Potts模型与大值的q不断发展的无标度网络，这个问题相当于一个最佳的合作问题。第三个检查的问题是有关的大q状态随机键Potts模型也和我检查的临界密度的集群接触的某个边界的一个垂直的带状几何形状，并期望持有解析形式推导出的共形不变性。最后一个研究问题是在零温无外场和Kosterlitz无相变点下二维三角晶格上反铁磁伊辛模型的非平衡动力学行为。
英文摘要：
In my PhD thesis I studied cooperative phenomena arise in complex systems using the methods of statistical and computational physics. The aim of my work was also to study the critical behaviour of interacting many-body systems during their phase transitions and describe their universal features analytically and by means of numerical calculations. In order to do so I completed studies in four different subjects. My first investigated subject was a study of non-equilibrium phase transitions in weighted scale-free networks. The second problem I examined was the ferromagnetic random bond Potts model with large values of q on evolving scale-free networks which problem is equivalent to an optimal cooperation problem. The third examined problem was related to the large-q sate random bond Potts model also and I examined the critical density of clusters which touched a certain border of a perpendicular strip like geometry and expected to hold analytical forms deduced from conformal invariance. The last investigated problem was a study of the non-equilibrium dynamical behaviour of the antiferromagnetic Ising model on two-dimensional triangular lattice at zero temperature in the absence of external field and at the Kosterlitz-Thouless phase transition point.
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