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Phys. Rev. E 66, 016104 (2002) [5 pages]

Ising model on networks with an arbitrary distribution of connections

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S. N. Dorogovtsev1,2 *, A. V. Goltsev2 †, and J. F. F. Mendes1 ‡
1 Departamento de Física and Centro de Física do Porto, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
2A.F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia

Received 10 March 2002; published 8 July 2002

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.


©2002 The American Physical Society

URL: http://link.aps.org/abstract/PRE/v66/e016104
DOI: 10.1103/PhysRevE.66.016104
PACS: 05.50.+q, 05.10.-a, 05.40.-a, 87.18.Sn

* Email address: sdorogov@fc.up.pt
† Email address: goltsev@pop.ioffe.rssi.ru
‡ Email address: jfmendes@fc.up.pt

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