# Phase transition in a network model of social balance with Glauber dynamics

## TL;DR

This paper investigates a social network model with Glauber-like dynamics, revealing a phase transition from bipolar to balanced states influenced by initial conditions and randomness, improving understanding of social balance evolution.

## Contribution

It introduces a more realistic dynamical model allowing escape from local minima, and identifies a sharp phase transition at initial link density, contrasting previous gradual transitions.

## Key findings

- System escapes frozen imbalanced states due to added randomness.
- A critical initial link density of 0.5 triggers a phase transition.
- Large networks exhibit a sharp transition from bipolar to paradise states.

## Abstract

We study the evolution of a social network with friendly/enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of $\rho_0^*=1/2$, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of $\rho_0^*=0.65$, observed in recent studies.