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The field-dependent magnetization m(H,T) of 1- and 2-dimensional classicalmagnets described by the $D$-component vector model is calculated analyticallyin the whole range of temperature and magnetic fields with the help of the 1/Dexpansion. In the 1-st order in 1/D the theory reproduces with a good accuracythe temperature dependence of the zero-field susceptibility of antiferromagnets\chi with the maximum at T \lsim |J_0|/D (J_0 is the Fourier component of theexchange interaction) and describes for the first time the singular behavior of\chi(H,T) at small temperatures and magnetic fields: \lim_{T\to 0}\lim_{H\to 0}\chi(H,T)=1/(2|J_0|)(1-1/D) and \lim_{H\to 0}\lim_{T\to 0}\chi(H,T)=1/(2|J_0|)

The 1/D expansion for classical magnets: Low-dimensional models with magnetic field