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arXiv 1104.0491cond-mat.stat-mechcond-mat.dis-nn
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Potts模型相变的加权网络粗粒度蒙特卡罗模拟

Coarse-grained Monte Carlo simulations of the phase transition of Potts model on weighted networks

Chuansheng Shen, Hanshuang Chen, Zhonghuai Hou, Houwen Xin

摘要:

发展有效的粗粒度(CG)方法是研究大规模网络动力学的一个很有前途的途径。本文提出了一种基于强度的CG(\sCG)方法来研究加权复杂网络上Potts模型的临界现象。通过将强度相近的节点合并到一起,将原网络简化为一个规模更小的CG-网络,在此网络上可以很好地定义CG-哈密尔顿算子。特别是,我们进行了误差分析,并表明我们的强度为基础的CG方法满足统计一致性的条件,这要求的CG模型的平衡概率分布相匹配的微观对应。在无标度网络上进行了大量的数值模拟,没有或有强度相关性,表明这种\sCG方法在再现微观模型的相图,波动和有限尺寸效应方面效果非常好,而我们最近的工作[Phys. Rev. E 82,011107(2010)]中提出的\dCG方法则没有。

英文摘要:

Developing effective coarse grained (CG) approach is a promising way for studying dynamics on large size networks. In the present work, we have proposed a strength-based CG (\sCG) method to study critical phenomena of the Potts model on weighted complex networks. By merging nodes with close strength together, the original network is reduced to a CG-network with much smaller size, on which the CG-Hamiltonian can be well-defined. In particular, we make error analysis and show that our strength-based CG approach satisfies the condition of statistical consistency, which demands that the equilibrium probability distribution of the CG-model matches that of the microscopic counterpart. Extensive numerical simulations are performed on scale-free networks, without or with strength-correlation, showing that this \sCG approach works very well in reproducing the phase diagrams, fluctuations, and finite size effects of the microscopic model, while the \dCG approach proposed in our recent work [Phys. Rev. E 82, 011107(2010)] does not.

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