Finite local moments

Tc (a -from their theory. Also the ratio n(T) of the mean square of the local moment at T to that at T = 0 remains finite at Tc whereas it vanishes for the Stoner-Wohlfarth theory, i.e. 

However, serious drawbacks of model 3 are that (i) the proportion r of the rotators should be fitted that is, it is not determined from physical considerations and (ii) the depth of the well, in which a polar particle moves, is considered to be infinite. Both drawbacks were removed in VIG (p. 305, 326, 465) and in Ref. 3, where it was assumed that (a) The potential is zero on the bottom of the well (/(()) = 0 at [ fi < 0 < P], where an angle 0 is a deflection of a dipole from the symmetry axis of a cone, (b) Outside the well the depth of the rectangular well is assumed to be constant (and finite) U(Q) = Uq at [— ti/2 < 0 < ti/2]. Actually, two such wells with oppositely directed symmetry axes were supposed to arise in the circle, so that the resulting dipole moment of a local-order region is equal to zero (as well as the total electric moment in any sample of an isotropic medium). 

Secondly, we can use the known fact that the disturbance (the displacement field) propagates in the elastic medium with a finite velocity. This means that if the disturbance is local at initial moment of time to (U (r, to) 7 0 only within some local domain), then it will be contained within a sphere of some finite radius r at any subsequent moment. The same observation holds true for the difference field U (r, t) as well. Therefore, considering the difference displacement field U (r, t) at some specified moment of time t > to, one can select an auxiliary sphere of the radius r large enough for the integral over the sphere Or in formula (13.154) to be equal to zero. From here, as it was previously discussed in the case of the bounded domain, it follows that relation (13.153) holds true, and the solution of the corresponding initial-value problem is unique. 

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