Ising Model on Networks with an Arbitrary Distribution of Connections
S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
Abstract
We find the exact critical temperature Tc of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution P(k). We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when P(k) is fat-tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, Tc approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.
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