Socio-economical dynamics as a solvable spin system on co-evolving networks

TL;DR

This paper models socio-economic dynamics using an exactly solvable spin system on co-evolving networks, revealing phase behaviors and the interplay between agent states and network structure.

Contribution

It introduces a novel exactly solvable model combining Ising spins and dynamic network links to analyze socio-economic interactions.

Findings

The model is exactly solvable due to binomial factorization of partition functions.

Phase diagrams are derived for finite and thermodynamic limits.

The interplay between agent states and network evolution influences system behavior.

Abstract

We consider social systems in which agents are not only characterized by their states but also have the freedom to choose their interaction partners to maximize their utility. We map such systems onto an Ising model in which spins are dynamically coupled by links in a dynamical network. In this model there are two dynamical quantities which arrange towards a minimum energy state in the canonical framework: the spins, s_i, and the adjacency matrix elements, c_{ij}. The model is exactly solvable because microcanonical partition functions reduce to products of binomial factors as a direct consequence of the c_{ij} minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discuss the phase diagrams.