Scaling corrections of Majority Vote model on Barabasi-Albert networks

TL;DR

This paper investigates the critical behavior of the Majority Vote model on Barabasi-Albert networks, revealing universal exponents with logarithmic corrections, contrasting with previous non-universal findings.

Contribution

It generalizes scaling relations to include logarithmic corrections and demonstrates the universality of critical exponents for the Majority Vote model.

Findings

Critical exponents are universal and independent of network connectivity.

Majority Vote and Biswas-Chatterjee-Sen models share the same universality class.

Majority Vote model exhibits logarithmic corrections, unlike the Biswas-Chatterjee-Sen model.

Abstract

We consider two consensus formation models coupled to Barabasi-Albert networks, namely the Majority Vote model and Biswas-Chatterjee-Sen model. Recent works point to a non-universal behavior of the Majority Vote model, where the critical exponents have a dependence on the connectivity while the effective dimension $D_\mathrm{eff} = 2\beta/\nu + \gamma/\nu$ of the lattice is unity. We considered a generalization of the scaling relations in order to include logarithmic corrections. We obtained the leading critical exponent ratios $1/\nu$, $\beta/\nu$, and $\gamma/\nu$ by finite size scaling data collapses, as well as the logarithmic correction pseudo-exponents $\widehat{\lambda}$, $\widehat{\beta}+\beta\widehat{\lambda}$, and $\widehat{\gamma}-\gamma\widehat{\lambda}$. By comparing the scaling behaviors of the Majority Vote and Biswas-Chatterjee-Sen models, we argue that the exponents of Majority Vote model, in fact, are universal. Therefore, they do not depend on network connectivity. In addition, the critical exponents and the universality class are the same of Biswas-Chatterjee-Sen model, as seen for periodic and random graphs. However, the Majority Vote model has logarithmic corrections on its scaling properties, while Biswas-Chatterjee-Sen model follows usual scaling relations without logarithmic corrections.