Small-world phenomena in physics: The Ising model

M. Gitterman

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The Ising system with a small fraction of random long-range interactions is the simplest example of small-world phenomena in physics. Considering the latter both in an annealed and in a quenched state we conclude that: (a) the existence of random long-range interactions leads to a phase transition in the one-dimensional case and (b) there is a minimal average number p of these interactions per site (p < 1 in the annealed state, and p ≃ 1 in the quenched state) needed for the appearance of the phase transition. Note that the average number of these bonds, pN/2, is much smaller than the total number of bonds, N2/2.

Original languageEnglish
Pages (from-to)8373-8381
Number of pages9
JournalJournal of Physics A: Mathematical and General
Issue number47
StatePublished - 1 Dec 2000


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