2011/04/04 by Chuansheng Shen, Hanshuang Chen, Zhonghuai Hou +1
Mathematics · Physics and Astronomy · #Artificial intelligence #Complex Network Analysis Techniques #Computer science #Consistency (knowledge bases) #Hamiltonian (control theory) #Hybrid Monte Carlo #Ising model #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Monte Carlo method #Opinion Dynamics and Social Influence #Phase transition #Physics #Potts model #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.83.066109
published as Physical Review E 83, 066109 (2011) · 7 pages, 4 figures
arxiv created 2011/04/04 · openalex publication_date 2011/06/16 · arxiv updated 2013/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Developing an 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 (s-CG) method to study critical phenomena of the Potts model on weighted complex networks. By merging nodes with close strengths 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 an error analysis and show that our s-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 and random networks, without or with strength correlation, showing that this s-CG approach works very well in reproducing the phase diagrams, fluctuations, and finite-size effects of the microscopic model, while the d-CG approach proposed in our recent work [Phys. Rev. E 82, 011107 (2010)] does not.