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

Abstract

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.

15 pages, two figures

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Cited by in corpus (6)

• Quantum memories at finite temperature
• A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
• Percolation on infinite graphs and isoperimetric inequalities
• Toward the mechanics of fractal materials: mechanics of continuum with fractal metric
• Non-equilibrium critical properties of the Ising model on product graphs
• Metric characterization of cluster dynamics on the Sierpinski gasket