Ising Model on Networks with an Arbitrary Distribution of Connections

Details Ising Model on Networks with an Arbitrary Distribution of Connections Ising Model on Networks with an Arbitrary Distribution of Connections

2002-03-11

arxiv.org/abs/cond-mat/0203227v3

Phys.Rev.E66:016104,2002

Physics

Condensed Matter

Statistical Mechanics

5 pages

Scientific paper

10.1103/PhysRevE.66.016104

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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