Non-equilibrium mean-field theories on scale-free networks

Abstract

Many non-equilibrium processes on scale-free networks present anomalous critical behaviorthat is not explained by standard mean-field theories. We propose a systematic method toderive stochastic equations for mean-field order parameters that implicitly account forthe degree heterogeneity. The method is used to correctly predict the dynamicalcritical behavior of some binary spin models and reaction–diffusion processes.The validity of our non-equilibrium theory is further supported by showing itsrelation with the generalized Landau theory of equilibrium critical phenomena onnetworks.