Reply to "Comment on 'Phase transition in a network model of social balance with Glauber dynamics' "

TL;DR

This paper defends the original findings of a social balance model with Glauber dynamics against recent critiques, clarifying the impact of energy definitions and updating rules on phase transition results.

Contribution

It clarifies the discrepancies caused by different energy definitions and updating rules, reaffirming the original phase transition findings in the social balance model.

Findings

Different energy definitions lead to contrasting results.

Synchronous and sequential updates significantly affect outcomes.

Original phase transition results are robust under proper conditions.

Abstract

Recently, we introduced [Physical Review E 100, 022303 (2019)] a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior. One important finding of our study was a phase transition from a balance state to an imbalance state as the randomness crosses a critical value, which was shown to vanish in the thermodynamic limit. In a recent similar study [K. Malarz and K. Ku\l akowskiy, (2020), arXiv:2009.10136], it was shown that the critical randomness tends to infinity as the system size diverges. This led the authors to question our results. Here, we show that this apparent inconsistency is the results of different definitions of energy in each model. We also demonstrate that synchronous and sequential updating rules can largely affect the results, in contrast with the claims made by the aforementioned authors.