TY - JOUR

T1 - Small-world phenomena in physics

T2 - The Ising model

AU - Gitterman, M.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034368612&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/33/47/304

DO - 10.1088/0305-4470/33/47/304

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AN - SCOPUS:0034368612

SN - 1751-8113

VL - 33

SP - 8373

EP - 8381

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 47

ER -