We report construction of a model of polar nanoregions in the PMN relaxor ferroelectric based on first-principles lattice dynamics for chemically ordered supercells [S.A. Prosandeev et al., Phys. Rev. B 70, 134110 (2004)], combined with invariance under permutations and dipole-dipole interaction as a source supporting randomly oriented residual polarization. Representative analytical estimates of polar nanore-gion - supercell mapping reproduce both nonzero local and zero macroscopic polarization of the structure, as well as the temperature change of the supercell anisotropy at cooling and field cooling.
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