Majority-vote model on triangular, honeycomb and Kagome lattices

Abstract

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.089(5), q_c=0.078(3), and q_c=0.114(2) for honeycomb, Kagome and triangular lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.15(5), 1.64(5), and 0.87(5); 0.14(3), 1.64(3), and 0.86(6); 0.12(4), 1.59(5), and 1.08(6) for honeycomb, Kagome and triangular lattices, respectively. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system D_{eff}= 1.96(5) (honeycomb), D_{eff} =1.92(4) (Kagome), and D_{eff}= 1.83(5) (triangular) for these networks are just compatible to the embedding dimension two.

5 pages, 5 figures, RevTeX4

References in corpus (15)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Evolution of networks
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Nonequilibrium Phase Transitions in Directed Small-World Networks
• Majority-vote model on random graphs
• Entropy production in the majority-vote model
• Majority-vote model on directed Erdos-Renyi random graphs
• Majority-vote model on hyperbolic lattices
• Majority-vote on directed Barabasi-Albert networks
• Majority-Vote Model on a Random Lattice
• Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices
• Majority-vote on directed Small-World networks
• Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

Cited by in corpus (14)

• Simple cubic random-site percolation thresholds for complex neighbourhoods
• Critical noise of majority-vote model on complex networks
• Three-state majority-vote model on square lattice
• Phase transition in the majority-vote model on the Archimedean lattices
• Exact solution of the isotropic majority-vote model on complete graphs
• Nonequilibrium Zaklan model on Apollonian Networks
• Critical phenomena in the majority voter model on two dimensional regular lattices
• Discontinuous phase transition in an annealed multi-state majority-vote model
• In search for the social hysteresis -- the symmetrical threshold model with independence on Watts-Strogatz graphs
• Large deviation induced phase switch in an inertial majority-vote model
• Antiferromagnetic majority voter model on square and honeycomb lattices
• The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer
• Majority-vote model with heterogeneous agents on square lattice
• Majority-vote model on Opinion-Dependent Networks