Expulsion from structurally balanced paradise

TL;DR

This study uses simulations to show that on a triangular lattice, systems starting from a balanced state tend to become unbalanced and disordered over time, unlike complete graphs where balance persists.

Contribution

It demonstrates that the triangular lattice topology prevents the emergence of Heider balance, contrasting with previous findings on complete graphs.

Findings

Triangular lattice prevents partial Heider balance.

Systems evolve from balanced to unbalanced states.

Relaxation time is independent of system size.

Abstract

We perform simulations of structural balance evolution on a triangular lattice using the heat-bath algorithm. In contrast to similar approaches---but applied to analysis of complete graphs---the triangular lattice topology successfully prevents the occurrence of even partial Heider balance. Starting with the state of Heider's paradise, it is just a matter of time when the evolution of the system leads to an unbalanced and disordered state. The time of the system relaxation does not depend on the system size. The lack of any signs of a balanced state was not observed in earlier investigated systems dealing with the structural balance.