Weiss Field Theory

Because of the decrease in Ma with increasing temperature, there is a change with temperature in the total exchange energy 

Equation 98 is known as the Bloch Tm law. It is in good agreement with experiment at very low temperatures other phenomena begin to appear at somewhat higher temperatures. An interesting phenomenon that demonstrates the existence of spin waves is the spin wave resonance spectrum recently observed in Permalloy films (554,612). 

At the Curie point, the Weiss theory predicts that for T Te, in the absence of an external field, the spin order vanishes completely. Actually there is considerable short-range order just above Te, as has been verified by neutron diffraction experiments (405,675). It is the problem of short-range order that is tackled by the more exact quantum statistics mentioned in connection with equation 94. At very high temperatures (T Te), there is no short-range order, and the experimental curve approaches the Curie-Weiss curve asymptotically. Theory shows that the possibility of short-range ordering lowers the 

For Jij 0, the Wa 0 and since action is equal to reaction, Wij = Wji. Since all interactions between sublattices are assumed to be contained within the Weiss field, it follows that the magnetization and the susceptibility of each sublattice are described by equations 91 and 95 provided the Weiss fields of equation 100 are used. 

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Fig. 15. Spontaneous magnetization vs. temperature, according to Weiss (655) theory, (a) Graphical solution. The value of M,/Mo is given by the intersection of the two curves, (b see facing page) Reduced-scale plot. The solid lines represent the Weiss field theory for J — 1/2, 1. The experimental (dashed) curves for iron and nickel fit more closely the theoretical curve for J = 1/2. (After Bozorth (92)).

MSN. 180. T. Petrosky and I. Prigogine, Limits to causality and delocalization in classical field theory, in Evolution Equations and Their Applications in Physical and Life Sciences, G. Lumer and L. Weis, eds., Marcel Decker, New York, 2000. 

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