Renormalization Group and Critical Exponents for Classical Heisenberg Ferromagnet with Dipole–Dipole Interaction

Abstract

The renormalization group technique is applied to the three-dimensional classical Heisenberg spin system with modified dipole-dipole interaction. For this system, the values and dependence of several critical exponents are investigated. These exponents are: a, the specific heat exponent; / 3 and 8, the magnetization exponents; y, the susceptibility exponent; 7, the correlation function exponent; and V , the correlation length exponent. All the critical exponents except @ depend upon the potential range IT. When the potential range u = 4, the modified dipole-dipole results agree with mean-field values of the critical exponents.Die Technik der Renormierungsgruppe wird auf das dreidimensionale, klassische Heisenberg-Spinsystem mit modifizierter Dipol-Dipol-Wechselwirkung angewandt. I n diesem System werden die Werte und die Abhangigkeit der verschiedenen kritischen Exponente untersucht. Diese Exponenten sind: a (der spezifische Warmeexponent), @ und 6 (die Magnetisierungsexponenten), y (der Suszeptibilitatsexponent), (der Exponent fur die Korrelationsfunktion) und v (der Exponent fur die Korrelationslange). Alle kritische Exponenten, aul3er &, hangen von der Potentialreichweite u ab. Falls die Potentialreichweite cr = t ist, stimmen die modifizierten Dipol-Dipol-Ergebnisse mit den gemittelten-Feld-Werten der kritischen Exponente uberein.

Nematic order in a simple-cubic lattice-spin model with full-ranged dipolar interactions

“…where σ ≥ 0 is a real parameter: all critical exponents with the exception of β were found to depend on σ, and the limiting case σ = 0 corresponded to the model studied here, for which Eqs. (47) in the named paper [49] yield α = 1, β = 1 2 , ν = 1, η = 2, γ = 0.…”

“…An interaction model defined by an extension of (1) had later been studied in [49] by RG; the interaction potential was defined by…”