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

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 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 (H, T) at small temperatures and magnetic fields: lim _T0 lim _H0 (H, T)=1/(2|J ₀|)(1–1/D) and lim _H0 lim _T0 (H, T)=1/(2|J ₀|).