Heider balance of a chain of actors as dependent on the interaction range and a thermal noise

TL;DR

This paper explores how the range of interactions and thermal noise influence the stability and dynamics of Heider balance in a chain of actors, revealing a transition between balanced and unbalanced states.

Contribution

It introduces a model analyzing Heider balance with variable interaction range and thermal noise, providing new insights into the energy spectrum and phase transition behavior.

Findings

Critical temperature increases with interaction range

Transition point independent of system size

Identifies spectrum of stationary and blinking states

Abstract

The Heider balance is investigated in a chain of actors, with periodic boundary conditions and the neighborhood of range $r$, with $r$ as a parameter. Two model dynamics are applied: a deterministic cellular automaton (Malarz et al, Physica D 411 (2020) 132556) and the heat-bath algorithm, with the density of unbalanced-balanced triads in the role of energy. The outcome is a spectrum of energy in stationary and blinking states and a balanced-unbalanced network transition driven by thermal noise. The critical point $T_c$ increases with the range $r$ and it does not depend on the system size.