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

TL;DR

This paper investigates the critical short-time dynamics of the majority-vote model on scale-free networks, combining theoretical mean-field analysis with Monte Carlo simulations to reveal non-universal and mean-field critical behaviors depending on network degree exponent.

Contribution

It introduces a heterogeneous mean-field theory for short-time behavior and compares it with simulations, providing new analytical expressions for dynamical exponents on scale-free networks.

Findings

Short-time scaling shows non-universal behavior for 2.5 < γ < 3.5.

For γ ≥ 3.5, the model exhibits mean-field Ising criticality.

Logarithmic corrections appear at γ=3.5, consistent with stationary scaling.

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 $\gamma \geq 7/2$, we have the mean-field Ising criticality with additional logarithmic corrections for $\gamma=7/2$, in the same way as the stationary scaling.