Ising Model on Networks with an Arbitrary Distribution of Connections
<|reference_start|>Ising Model on Networks with an Arbitrary Distribution of Connections: 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.<|reference_end|>
@article{dorogovtsev2002ising,
    title={Ising Model on Networks with an Arbitrary Distribution of Connections},
    author={S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes},
    journal={Phys.Rev.E66:016104,2002},
    year={2002},
    doi={10.1103/PhysRevE.66.016104},
    archivePrefix={arXiv},
    eprint={cond-mat/0203227},
    primaryClass={cond-mat.stat-mech cs.NI hep-lat hep-th math-ph math.MP nlin.SI physics.class-ph}
}