Majority-vote model on random graphs

TL;DR

This paper investigates the majority-vote model with noise on random graphs, analyzing phase transitions and critical exponents through Monte Carlo simulations, revealing how connectivity influences critical noise and confirming hyperscaling relations.

Contribution

It provides new insights into how the mean connectivity affects phase transition properties and critical exponents in the majority-vote model on random graphs.

Findings

Critical noise increases with mean connectivity.

Critical exponents satisfy hyperscaling with effective dimension one.

Phase transition characteristics depend on graph connectivity.

Abstract

The majority-vote model with noise on 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 is an increasing function of the mean connectivity of the random graph. The critical exponents beta/nu, gamma/nu and 1/nu were calculated for several values of z, and our analysis yielded critical exponents satisfying the hyperscaling relation with effective dimensionality equal to unity.