Socio-economical dynamics as a solvable spin system on co-evolving networks
نویسندگان
چکیده
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, si, and the adjacency matrix elements, cij . The model is exactly solvable because microcanonical partition functions reduce to products of binomial factors as a direct consequence of the cij minimizing energy. We solve the system for finite sizes and for the two possible thermodynamic limits and discuss the phase diagrams. PACS. 87.23.Ge Dynamics of social systems – 89.75.Fb Structures and organization in complex systems – 05.90.+m Networks and genealogical trees – 75.10.Hk Classical spin models – 75.10.Nr Spin-glass and other random models
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