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

The field-dependent magnetization m(H, T) of one- and two-dimensional classical magnets described by the D-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 chi with maximum al T less than or similar to \J(0)\/D (J(0) is the Fourier component of the exchange interaction) and describes for the first time the singular behavior of chi(H, T) at small temperatures and magnetic fields: lim(T-->0) lim(H-->0) chi(H, T) = 1/(2 \J(0)\)(1-1/D) and lim(H-->0) lim(T-->0) chi(X, T) = 1/(2 \J(0)\).