  We propose a statistical mechanics approach to a coevolving spin system with
an adaptive network of interactions. The dynamics of node 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 the complex behavior
of real-world systems and omitting one of the approaches renders the
description incomplete.
