Comment on `Phase transition in a network model of social balance with Glauber dynamics'

TL;DR

This paper revisits the critical temperature of a social balance network model, finding that it increases with network size, contrasting previous results that suggested it decreases.

Contribution

It introduces a heat-bath algorithm approach to compute the critical temperature, revealing its growth with network size and dependence on initial conditions.

Findings

Critical temperature increases with network size as N^γ.

The exponent γ is approximately 0.5 or 1.0.

Dependence of T_c on initial bond fractions.

Abstract

In a recent work [R. Shojaei et al, Physical Review E 100, 022303 (2019)] the Authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings, $T_c$ decreases with the number of nodes $N$. Here we calculate the same critical temperature using the heat-bath algorithm. We show that $T_c$ increases with $N$ as $N^{\gamma}$, with $\gamma$ close to 0.5 or 1.0. This value depends on the initial fraction of positive bonds.