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Ising Model on Networks with an Arbitrary Distribution of Connections

S. N. Dorogovtsev·A. V. Goltsev·J. F. F. Mendes
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Abstract

We find the exact critical temperature $T_c$ 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, $T_c$ approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.

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S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes. 2002-04-11. Ising Model on Networks with an Arbitrary Distribution of Connections. https://doi.org/10.1103/physreve.66.016104

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