Eur. Phys. J. B 67, 285-289 (2009)
https://doi.org/10.1140/epjb/e2008-00390-7

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

¹ Complex Systems Research Group, HNO, Medical University of Vienna, Währinger Gürtel 18-20, 1090 Vienna, Austria
² Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

Corresponding author: ^a thurner@univie.ac.at

Received: 2 April 2008
Revised: 29 August 2008
Published online: 18 October 2008

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.