Organization and Complexity in a Nested Hierarchical Spin-Glass like Social Space

TL;DR

This paper models complex social systems as hierarchical spin-glass-like energy landscapes, analyzing how identities form and change across multiple levels with many variables, revealing dynamic reorganization behaviors.

Contribution

It introduces a novel mathematical framework combining spin-glass physics with hierarchical social interactions, accounting for multiple variables per agent and cross-level influences.

Findings

Identifies conditions for identity persistence and change.

Shows how hierarchy influences social dynamics.

Highlights complex reorganization patterns.

Abstract

In this paper, we mathematically formulate the interaction and dynamics of a hierarchical complex social system where each agent is seen as an array of many variables. The formation of identities and modifications can be studied by using interaction physics in an energy landscape. The spin glass Hamiltonian is modified to suit our needs in light of complexity. The expression of variables subject to weights and topology is considered. Interactions within the same hierarchy level as well as the effect of one hierarchy level on another are studied. The effect of having many variables associated with a single agent brings about interesting dynamics. The persistence of the identity units subject to stiffness, continuous changes and also sudden reorganizations is discussed.