Critical exponents of ferromagnets with dipolar interactions: Second-order ε expansion

Alastair D. Bruce*, Amnon Aharony

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


The zero-field critical behavior of ferromagnets above Tc, with both isotropic exchange coupling and dipolar interactions, is studied by renormalization-group techniques in d=4-ε dimensions with n(=d) component spins. The critical exponents are calculated to order ε2, and are found to be numerically very close to their nondipolar analogs. In particular the correlation length exponent is given by 2ν=1+(934)ε+(701358956) ε2+O(ε3). The value of the specific-heat exponent αs (=2-dν) seems inconsistent with experimental data (at d=3, ε=1). The critical scattering function is shown to have the form Γαβ(q→)=Ct- γD^(ξ2q2)(δαβ-qαqβq2) to all orders in ε. The exponents related to the leading correction to scaling, to crossovers to anisotropic exchange behavior, and to cubic dipolar behavior, are also calculated, and are found to differ significantly from their nondipolar counterparts.

Original languageEnglish
Pages (from-to)2078-2087
Number of pages10
JournalPhysical Review B-Condensed Matter
Issue number5
StatePublished - 1974
Externally publishedYes


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