2009/02/18 by Yilong Han · 2 citations
Mathematics · Physics and Astronomy · #Antiferromagnetism #Artificial intelligence #Class (philosophy) #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Condensed matter physics #Ergodic theory #Frustration #Gaussian #Geometry #Homogeneous space #Ising model #Lattice (music) #Mathematics #Opinion Dynamics and Social Influence #Phase (matter) #Phase space #Physics #Pure mathematics #Quantum mechanics #Space (punctuation) #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.80.051102
arxiv created 2009/02/18 · openalex publication_date 2009/11/05 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.