Ising Model on Networks with an Arbitrary Distribution of Connections

2002/03/31 by S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes
Physics and Astronomy · Computer Science · Mathematics · #cond-mat.stat-mech #cs.NI #hep-lat #hep-th #math-ph #math.MP #nlin.SI #physics.class-ph

paper · pdf · doi:10.1103/physreve.66.016104

published as Phys.Rev.E66:016104,2002 · 5 pages

arxiv created 2002/04/11 · arxiv updated 2016/08/31

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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