We propose a statistical mechanics approach to a coevolving spin system with adaptive network of interactions.
The dynamics of nodes' states and network connections is driven by both spin configuration and network topology.
We consider a hamiltonian that merges the classical Ising model and the statistical theory of correlated random networks.
As a result, we obtain rich phase diagrams with different phase transitions both in the state of nodes and in the graph topology.
We argue that the coupling between the spin dynamics and the structure of the network is crucial in understanding complex behavior of the real-world systems, and omitting one of the approaches renders the description incomplete

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