Mean-field approximation and phase transitions in an Ising-voter model on directed regular random graphs

Abstract

It is known that on directed graphs, the correlations between neighbours of a given site vanish and thus simple mean-field-like arguments can be used to describe exactly the behaviour of Ising-like systems. We analyse heterogeneous modifications of such models where a fraction of agents is driven by the voter or the antivoter dynamics. It turns out that voter agents do not affect the dynamics of the model and it behaves like a pure Ising model. Antivoter agents have a stronger impact since they act as a kind of noise, which weakens a ferromagnetic ordering. Only when Ising spins are driven by the heat-bath dynamics, the behaviour of the model is correctly described by the mean-field approximation. The Metropolis dynamics generates some additional correlations that render the mean-field approach approximate. Simulations on annealed networks agree with the mean-field approximation but for the model with antivoters and with the Metropolis dynamics only its heterogeneous version provides such an agreement. Calculation of the Binder cumulant confirms that critical points in our models with the heat-bath dynamics belong to the Ising mean-field universality class. For the Metropolis dynamics, the phase transition is most likely discontinuous, at least for not too many antivoters.

11 pages

References in corpus (23)

• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Statistical physics of social dynamics
• Epidemic processes in complex networks
• Random graphs with arbitrary degree distributions and their applications
• Non-reciprocal phase transitions
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Giant strongly connected component of directed networks
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• High-accuracy approximation of binary-state dynamics on networks
• Reality Inspired Voter Models: A Mini-Review
• Epidemic threshold for the SIS model on networks
• Binary-state dynamics on complex networks: pair approximation and beyond
• Nonequilibrium Phase Transitions in Directed Small-World Networks
• Social applications of two-dimensional Ising models
• Non-Hermitian Localization in Biological Networks
• Parallel dynamics of disordered Ising spin systems on finitely connected random graphs
• Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions
• Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models
• Phase transition and power-law coarsening in Ising-doped voter model
• Phase transitions in Ising models on directed networks
• Equilibrium behavior in a nonequilibrium system: Ising-doped voter model on complete graph
• Heat-Bath and Metropolis Dynamics in Ising-like Models on Directed Regular Random Graphs