Is the theory of spin waves any better than the Weiss molecular field theory of ferromagnets?
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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 staticenergetically-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 elementaryexcitations 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
Mean-field theories with a magnetic order-parameter (like the Curie-Weiss theory) only describe the staticenergetically-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 elementaryexcitations 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
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Yes yes theory of pin waves is any better than the molecular field theory of four magnets
jacobcunningham202:
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