2009/11/02 by Zhi-Xi Wu, Petter Holme
Mathematics · Physics and Astronomy · #Boundary value problem #Complex Network Analysis Techniques #Condensed matter physics #Critical exponent #Curse of dimensionality #Ising model #Lattice (music) #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Periodic boundary conditions #Phase transition #Physics #Quantum mechanics #Renormalization group #Statistical physics #Statistics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.stat-mech #physics.soc-ph
paper · pdf · doi:10.1103/physreve.81.011133
published as Phys.Rev.E 81, 011133 (2009). · 8 pages, 9 figures
arxiv created 2009/11/02 · openalex publication_date 2010/01/26 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the critical properties of a nonequilibrium statistical model, the majority-vote model, on heptagonal and dual heptagonal lattices. Such lattices have the special feature that they only can be embedded in negatively curved surfaces. We find, by using Monte Carlo simulations and finite-size analysis, that the critical exponents 1/nu , beta/nu , and gamma/nu are different from those of the majority-vote model on regular lattices with periodic boundary condition, which belongs to the same universality class as the equilibrium Ising model. The exponents are also from those of the Ising model on a hyperbolic lattice. We argue that the disagreement is caused by the effective dimensionality of the hyperbolic lattices. By comparative studies, we find that the critical exponents of the majority-vote model on hyperbolic lattices satisfy the hyperscaling relation 2beta/nu+gamma/nu=D(eff), where D(eff) is an effective dimension of the lattice. We also investigate the effect of boundary nodes on the ordering process of the model.