Mean-Field Solution for Critical Behavior of Signed Networks in Competitive Balance Theory

TL;DR

This paper applies mean-field theory to analyze the critical behavior of competitive balance in signed networks, revealing a phase transition where one interest dominates at a critical temperature, supported by simulations.

Contribution

It introduces a mean-field analytical approach to study phase transitions in competitive balance models of signed networks, extending thermal balance theory.

Findings

Spontaneous symmetry breaking at a critical temperature.

Critical temperature scales linearly with network size.

Simulation results confirm mean-field predictions.

Abstract

Competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks arXiv:2001.04664 . In this model two different paradigms compete with each other due to the competitive interests to dominate the system and impose their own values. Using mean-field solution method in this paper, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competitive interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to ultimately decrease tension stemming from balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the network. The critical temperature depends linearly on the number of nodes, which was a linear dependence in the thermal balance theory as well. Finally the results obtained through the mean-field theory are verified by a series of simulations.