Critical Short-Time Behavior of Majority-Vote Model on Scale-Free Networks

Abstract

We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. We introduce a heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free networks. In addition, we also compare the heterogeneous mean-field predictions with extensive Monte Carlo simulations of the short-time dependencies of the order parameter and the susceptibility. We obtained a closed expression for the dynamical exponent $z$ and the time correlation exponent ${\nu }_{\parallel }$. Short-time scaling is compatible with a non-universal critical behavior for $5/2<\gamma <7/2$, and for $\gamma \ge 7/2$, we have the mean-field Ising criticality with additional logarithmic corrections for $\gamma =7/2$, in the same way as the stationary scaling.

10 pages, 3 figures, 24 references