Generalization of the Peierls-Griffiths Theorem for the Ising Model on Graphs

We present a sufficient condition for the presence of spontaneous magnetization for the Ising model on a general graph, related to its long-range topology. Applying this condition we are able to prove the existence of a phase transition at temperature T > 0 on a wide class of general networks. The possibility of further extensions of our results is discussed.