Decoupled-mode dynamical scaling theory of the ferromagnetic phase transition

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Abstract
The dynamical scaling theory of phase transitions begins below the phase transition and extrapolates the frequencies, by means of the temperature continuity at a finite wave number, through the critical point into the temperature region above the transition. Applied to the ferromagnet, this approach leads to the observed five-halves critical dispersion at the Curie point. In the paramagnetic region it yields the critical slowing down of spin diffusion with a critical exponent of one-third. An alternative approach beginning in the paramagnetic region has been developed from the basic statistical mechanics of spin interaction. In the present paper, we present a simplified version of this approach, based on the fluctuation-dissipation theorem. The relevant form of this theorem is easily derived along familiar lines and involves obtaining an expression for the spin current. The spin diffusi on coefficient is then expressed in terms of the ratio of the fluctuations in spin current aud spin density. The correlation function for the current fluctuations can be evaluated by factoring (decoupled-mode approximation). The results are shown to be equivalent of those obtained by the other methods, and a simple explanation is given for the rise of the scaling function outside of the hydrodynamic region