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The study of systems of interacting networks has been growing in the last decades, due to theirs the wide range of applications. In the context of statistical mechanics, one of the main interests in different architectures of interacting networks lies in the study of emergent macroscopic phenomena and phase transitions. In this work we investigate the cooperative behavior and phase transitions of systems of Ising spin interacting through different architectures. In this class of models, each node of the network takes on a binary value reflecting some variable – an opinion on some binary decision or choice, for example. In many models of opinion dynamics, the system eventually evolves to a consensus, all individuals having the same opinion. The first architecture consists of two coupled Erdös-Rényi random graphs with finite connectivity and ferromagnetic interactions. We obtain analytical expressions for the free energy of the system and the magnetization of each graph, from which we construct the phase diagrams that make evident the presence of three different solutions: a paramagnetic state, where the magnetization of each graph is zero; a ferromagnetic solution, where the magnetization of each graph has the same sign; and an anti-aligned phase, where the graphs have magnetizations with opposite signs. Based on the calculation of the free energy, we show that this model has a metastable solution, where the anti-aligned state corresponds to a local minimum of the free energy, while the ferromagnetic state is the global minimum. By performing Monte-Carlo simulations, we confirm the exactness of 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. We also discuss the effect of different architectures, such as modular and core-periphery structures, on the phase diagram of the Ising model coupled defined on regular graphs.