  We explore the cooperative behaviour and phase transitions of interacting
networks by studying a simplified model consisting of Ising spins placed on the
nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical
expressions for the free-energy of the system and the magnetization of each
graph, from which the phase diagrams, the stability of the different states,
and the nature of the transitions among them, are clearly characterized. We
show that a metastable state appears discontinuously by varying the model
parameters, yielding a region in the phase diagram where two solutions coexist.
By performing Monte-Carlo simulations, we confirm the exactness of our main
theoretical results and show that the typical time the system needs to escape
from a metastable state grows exponentially fast as a function of the
temperature, characterizing ergodicity breaking in the thermodynamic limit.
