Majority-vote model on random graphs

Abstract

The majority-vote model with noise on Erdös-Rényi's random graphs has been studied. Monte Carlo simulations were performed to characterize the order-disorder phase transition appearing in the system. We found that the value of the critical noise parameter qc is an increasing function of the mean connectivity z of the random graph. The critical exponents β/ν, γ/ν and 1/ν were calculated for several values of z, and our analysis yielded critical exponents satisfying the hyperscaling relation with effective dimensionality equal to unity.

Majority-vote model on hyperbolic lattices

“…Oliveira first verified this conjecture on a square lattice with periodic boundary conditions (i.e., a torus) [14]. Subsequently, the majority-vote model has been investigated on regular lattices (with dimension larger than two) [16,17,19,20], random lattice [21], directed or undirected random graphs [22,23], small world networks [24], and scale-free networks [25], etc. Very recently, it has been found that the critical behavior of the majority-vote model on square lattice is also independent of transition rates (e.g., the Glauber or Metropolis rates) [19].…”

Controlling the Tax Evasion Dynamics via Majority-Vote Model on Various Topologies

“…To their surprise all results obtained for the critical exponents are different from results obtained by M. J. Oliveira, and are also different for each topology used. Pereira et al [49] then concluded that MVM has different universality classes which depend only on the topology used, and that all have one thing in common that is their effective dimension, obtained by critical exponents for each topology used, equals Deff = 1. Here, we show that the Zaklan model behavior is identical for all topologies or dynamics studied here.…”

Modelling behavioural contagion

“…Where a is close to n/2, then there will be similarities between these transmission dynamics and majority vote models (e.g. [11,12]) although behaviour cessation will be qualitatively different.…”

“…Modelling techniques have so far typically involved either explicit stochastic simulation [3 -6], or else application of mathematical models originally developed for other applications, such as the Susceptible-Infectious-Susceptible (SIS) epidemic model considered by Kiss et al [7] and Funk et al [8]. An alternative is to use a discrete-time formalism [9,10], next-generation arguments [5] or methods from statistical physics [11,12] to obtain results about asymptotic behaviour of socially motivated models, although typically calculating transient features of system dynamics requires Monte Carlo simulation.…”