We study the coevolution of a generalized Glauber dynamics for Ising spins,
with tunable threshold, and of the graph topology where the dynamics takes
place. This simple coevolution dynamics generates a rich phase diagram in the
space of the two parameters of the model, the threshold and the rewiring
probability. The diagram displays phase transitions of different types: spin
ordering, percolation, connectedness. At variance with traditional coevolution
models, in which all spins of each connected component of the graph have equal
value in the stationary state, we find that, for suitable choices of the
parameters, the system may converge to a state in which spins of opposite sign
coexist in the same component, organized in compact clusters of like-signed
spins. Mean field calculations enable one to estimate some features of the
phase diagram.Comment: 5 pages, 3 figures. Final version published in Physical Review