Abstract
The field-dependent magnetizationm(H, T) of one- and two-dimensional classical magnets described by theD-component vector model is calculated analytically in the whole range of temperature and magnetic fields with the help of the 1/D expansion. In the first order in 1/D the theory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets χ with maximum atT≲|J 0|/D (J 0 is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of χ(H, T) at small temperatures and magnetic fields: lim T→0 lim H→0 χ(H, T)=1/(2|J 0|)(1−1/D) and lim H→0 lim T→0 χ(H, T)=1/(2|J 0|).
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Garanin, D.A. The 1/D expansion for classical magnets: Low-dimensional models with magnetic field. J Stat Phys 83, 907–931 (1996). https://doi.org/10.1007/BF02179549
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DOI: https://doi.org/10.1007/BF02179549