The phase diagram and critical behavior of the three-state majority-vote model

Abstract

The three-state majority-vote model with noise on Erdos-Renyi's random graphs has been studied. Using Monte Carlo simulations we obtain the phase diagram, along with the critical exponents. Exact results for limiting cases are presented, and shown to be in agreement with numerical values. We find that the critical noise qc is an increasing function of the mean connectivity z of the graph. The critical exponents beta/nu, gamma/nu and 1/nu are calculated for several values of connectivity. We also study the globally connected network, which corresponds to the mean-field limit z = N-1 -> infinity. Our numerical results indicate that the correlation length scales with the number of nodes in the graph, which is consistent with an effective dimensionality equal to unity.

References in corpus (13)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Statistical physics of social dynamics
• Finite-size scaling in complex networks
• Majority-vote model on random graphs
• 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
• Short time dynamics of a two dimensional majority vote model
• Majority-vote on directed Small-World networks
• Cumulants of the three state Potts model and of nonequilibrium models with C3v symmetry
• Corrections to finite-size scaling in two-dimensional O(N) sigma-models

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• Majority vote model with ancillary noise in complex networks
• Majority-vote model with limited visibility: an investigation into filter bubbles
• Non-Markovian Majority-Vote model
• Majority-vote model on spatially embedded networks: crossover from mean-field to Ising universality classes
• Explosive Phase Transition in a Majority-Vote Model with Inertia
• Phase transitions in a multistate majority-vote model on complex networks
• Finite-size effects on the convergence time in continuous-opinion dynamics
• Three-state Majority-Vote Model on Barabási-Albert and Cubic Networks and the Unitary Relation for Critical Exponents