The phase diagram and critical behavior of the three-state majority-vote model

TL;DR

This paper investigates the phase transitions and critical behavior of the three-state majority-vote model with noise on Erdos-Renyi random graphs, providing phase diagrams, critical exponents, and insights into the model's universality class.

Contribution

The study offers the first comprehensive analysis of the three-state majority-vote model on random graphs, including phase diagrams, critical exponents, and the effect of connectivity on critical noise.

Findings

Critical noise increases with mean connectivity.

Critical exponents vary with connectivity.

Correlation length scales with system size, indicating effective one-dimensionality.

Abstract

The three-state majority-vote model with noise on Erdos-Renyi's random graphs has been studied. Using Monte Carlo simulations we obtain the phase diagram, along with the critical exponents. Exact results for limiting cases are presented, and shown to be in agreement with numerical values. We find that the critical noise qc is an increasing function of the mean connectivity z of the graph. The critical exponents beta/nu, gamma/nu and 1/nu are calculated for several values of connectivity. We also study the globally connected network, which corresponds to the mean-field limit z = N-1 -> infinity. Our numerical results indicate that the correlation length scales with the number of nodes in the graph, which is consistent with an effective dimensionality equal to unity.