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Random local field method for the description of physical properties of disordered solids. (English) Zbl 1371.82045
Summary: We suggest an approach to describe the physical properties of disordered dielectric and/or magnetic systems. These systems are characterized by randomly positioned and oriented spins (dipoles) in a host crystal lattice. The ensemble of these spins or dipoles create the random magnetic or electric fields in a host lattice. Their distribution function, defined as an average (over spatial and orientational fluctuations) of Dirac delta contributions of each spin (dipole), enables us to obtain the self-consistent equations for order parameters like average magnetization (polarization) $$\langle S\rangle$$, and/or general quantities like $$\langle S^n\rangle$$. We calculate explicitly the above distribution functions for different types of interactions and show that, in general, they are not Gaussian. Our theory delivers pretty good description of experiments in disordered ferroelectrics, multiferroics, magnets and diluted magnetic semiconductors.
##### MSC:
 82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
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