United v.s. Divided, Deconfinement of Social Tension as a Topological Phase Transition

TL;DR

This paper models social tension as a topological phase transition using Ising lattice gauge theory, revealing how rule-breakers can cause societies to shift between united and divided phases with distinct structural behaviors.

Contribution

It introduces a novel application of topological phase transition theory to social networks, linking social tension dynamics to Ising lattice gauge models and phase behavior.

Findings

In the united phase, rule-breakers cause local rearrangements.

In the divided phase, rule-breakers lead to societal fragmentation.

Social tension behaves as $Z_2$ topological defects, confined or deconfined depending on the phase.

Abstract

The proverbs "the enemy of my enemy is my friend" and alike capture the essence of many body correlations in social relations, whose violation leads to social tension. We study how rule-breakers, who disrespect these norms, affect the structure and dynamics of signed social networks which tries to minimize social tension. We find two dynamic phases. A friendly society exhibits a "united phase" where insertion of a rule-breaker only leads to localized rearrangement. A hostile society exhibits a "divided phase", where insertion leads to macroscopic reorganization of social relations. In the divided phase, starting from the utopia state, where all relations are friendly, insertion of a {\em separatist}, a particular type of rule-breaker who makes friends with only half of its neighbors, leads to fragmentation, where the society breaks into many finite size, mutually antagonistic cliques. These phenomena are described by Ising lattice gauge theory, where social tension behave as $Z_2$ topological defects, which are confined in the united phase and deconfined in the divided phase. We further show that the connection between social dynamics and Ising lattice gauge theory is viable independently of connectivity structure of the social network.