Effective magnetic field parameter approximation

Applying superposition approximations to the Ising model, one finds an evidence for the phase transition existence but the critical parameter to is systematically underestimated (To is overestimated respectively). Errors in calculation of to are greater for low dimensions d. Therefore, the superposition approximation is effective, first of all, for the qualitative description of the phase transition in a spin system. In the vicinity of phase transition a number of critical exponents a, /3,7,..., could be introduced, which characterize the critical point, like oc f-for . M oc (i-io), or xt oc i—io for the magnetic permeability. Superposition approximations give only classical values of the critical exponents a = ao, 0 = f o, j — jo, ., obtained earlier in the classical molecular field theory [13, 14], say fio = 1/2, 7o = 1, whereas exact magnitudes of the critical exponents depend on the space dimension d. To describe the intermediate order in a spin system in terms of the superposition approximation, an additional correlation length is introduced, 0 = which does not coincide with the true In the phase... 

In all single-crystal studies, the variation in resonance frequency or magnetic field is studied as a function of the orientation of the crystal in the magnetic field. A spin Hamiltonian of appropriate form is then solved and the parameters adjusted to fit the calculated variation with the experimental data. Most errors in doing this occur because approximate solutions of spin Hamiltonians are used for systems for which the approximations are not justified. Second-order effects are often very important in analyzing single-crystal ESR and ENDOR measurements. 

In general, however, optical dielectric anisotropy and its dc or low-frequency counterpart (the dielectric anisotropy) provide a less rehable measure of the order parameter because they involve electric fields. This is because of the so-called local field effect the effective electric field acting on a molecule is a superposition of the electric field from the externally apphed source and the field created by the induced dipoles surrounding the molecules. For systems where the molecules are not correlated, the effective field can be fairly accurately approximated by some local field correction factor in liquid ciystalline systems these correction factors are much less accurate. For a more reliable determination of the order parameter, one usually employs non-electric-field-related parameters, such as the magnetic susceptibiUty anisotropy ... 

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