2003/03/31 by U. Krey
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Law #Physics #Physics of Superconductivity and Magnetism #Political science #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Statistical physics #Theoretical physics #Universality (dynamical systems) #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0304-8853(03)00534-1
LATEX, 27 pages (including 5 eps-figures); accepted by JMMM
arxiv created 2003/06/08 · openalex publication_date 2003/07/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The apparent universality of Bloch's T3/2-law for the temperature dependence of the spontaneous magnetization, and of generalizations thereof, is considered. It is argued that in the derivation one should not only consider the exchange interaction between the spins, but also the other interactions between them, leading to elliptical spin precession and deviations from the parabolic dispersion of magnons. Also interaction effects are important to explain the apparent universality of generalized Bloch law exponents eB, defined by Ms(T)= Ms(0)-const. x TeB, valid in a wide temperature range T1 < T < T2, and for dimensionalities d = 1, 2, and 3. The above-mentioned temperature range, the 'Bloch range', lies above the quantum range, where magnetic long-range order (e.g. in d=2 dimensions) is nontrivially enforced by the additional interactions, but below the thermal critical region, where universal 'anomalous scaling dimensions' apply. In contrast, for the Bloch temperature region, the universality is only apparent, i.e. a crossover-phenomenon, and simple scaling considerations with 'normal dimensions' apply. However, due to interactions, the Bloch exponent eB depends not only on the dimensionality d of the system, but also on the spin quantum number s (mod (1/2)) of the system, i.e. for given d the Bloch exponent eB is different for half-integer s and for integer s.