Is the theory of spin waves any better than the Weiss molecular field theory of ferromagnets? I was aware of Weiss molecular field theory of ferromagnetism and have recently been exposed to the theory of spin waves of ferromagnetism. It is expected that there should be some drawbacks of Weiss theory because it doesn't take the detailed interactions of the neighbouring atomic moments into account. Does the theory of spin waves amend the drawbacks of Weiss molecular field theory (if any) and address experimental features that the Weiss theory cannot? 
 A: Both spin-density-wave (SDW) theory and Curie-Weiss mean-field theory are based on an assumption a priori that the ground-state and excitations of an interacting system of particles with magnetic moments (spin or otherwise) can be described in terms of (uniform or wave-like) configurations of the orientation of the magnetic moments — whether such a picture is correct or not can only be determined via experimental results; for details (also experimental), see chp. 4 of Grüner, “Density Waves in Solids” (2000) [wcat].
Mean-field theories with a magnetic order-parameter (like the Curie-Weiss theory) only describe the static energetically-preferred magnetic configuration of the system at a vanishing (or very low) temperature. It is assumed that the magnetic moments point rigidly in the direction determined by the effective mean-field.
However, although a mean-field analysis is the first step to understand the physics of magnetic systems, it will not provide a correct physical picture, because fluctuations (thermal or quantum) are always present in the systems of interest. Here is where spin-density-wave analysis comes to rescue as an attempt to describe the behaviour of collective magnetic excitations.
From a theoretical point of view, spin-density-wave theory goes beyond a mean-field theory to include and describe fluctuations or even, interactions between the spin-density waves as the elementary excitations of the system. So, spin-density-wave theory can describe phases that mean-field can't. In interacting 1D electronic systems, for instance, where mean-field theory fails miserably, spin-density waves (plus an exotic separation between charge- and spin- density waves) can be obtained via exact solutions; see eg., Giamarchi, “Quantum physics in one dimension” (2006) [wcat].
This is, in fact, quite analogous to going beyond the rigid-lattice approximation, and considering the vibrations of the ions about their equilibrium positions to understand the thermal properties of crystals in terms of phonons.
For a detailed discussion of the classical and quantum spin-wave theory, consult chp. 14 of Sólyom, “Fundamentals of the Physics of Solids”. vol. I (2007) [wcat].
