Majority-vote model on hyperbolic lattices

Abstract

We study the critical properties of a non-equilibrium 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 $2\beta /\nu +\gamma /\nu =D_{\mathrm{eff}}$, where $D_{\mathrm{eff}}$ is an effective dimension of the lattice. We also investigate the effect of boundary nodes on the ordering process of the model.

8 pages, 9 figures

References in corpus (10)

• Nonequilibrium phase transition in the coevolution of networks and opinions
• Majority-vote model on directed Erdos-Renyi random graphs
• Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices
• Percolation on hyperbolic lattices
• Curvature-induced frustration in the $XY$ model on hyperbolic surfaces
• Phase Transition of XY Model in Heptagonal Lattice
• Tricritical point of J1-J2 Ising model on hyperbolic lattice
• Phase transition of $q$-state clock models on heptagonal lattices
• Phase transition of clock models on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Diffusion on a heptagonal lattice

Cited by in corpus (21)

• The structure and dynamics of multilayer networks
• Critical noise of majority-vote model on complex networks
• Phase transitions in the majority-vote model with two types of noises
• Enhancement of cooperation through conformity-driven reproductive ability
• The phase diagram and critical behavior of the three-state majority-vote model
• Majority-vote model on triangular, honeycomb and Kagome lattices
• Critical phenomena of the Majority voter model in a three dimensional cubic lattice
• Impact of site dilution and agent diffusion on the critical behavior of the majority-vote model
• Nonequilibrium Zaklan model on Apollonian Networks
• Crossing on hyperbolic lattices
• Phase transition and power-law coarsening in Ising-doped voter model
• Critical phenomena in the majority voter model on two dimensional regular lattices
• Non-Markovian Majority-Vote model
• Discontinuous phase transition in an annealed multi-state majority-vote model
• Phase transitions in a multistate majority-vote model on complex networks
• Explosive Phase Transition in a Majority-Vote Model with Inertia
• Quenched mean-field theory for the majority-vote model on complex networks
• Large deviation induced phase switch in an inertial majority-vote model
• Diffusive Majority Vote Model
• The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer
• An alternative order-parameter for non-equilibrium generalized spin models on honeycomb lattices