  The apparent universality of Bloch's T^{3/2}-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 e_B,
defined by M_s(T)= M_s(0)-const. x T^{e_B}, valid in a wide temperature range
T_1 < T < T_2, 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 e_B 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 e_B is different for
half-integer s and for integer s.
