THE 1 D EXPANSION FOR CLASSICAL MAGNETS - LOW-DIMENSIONAL MODELS WITHMAGNETIC-FIELD/

The field-dependent magnetization m(H, T) of one- and two-dimensional classical magnets described by the D-component vector model is calcula ted 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 the ory reproduces with a good accuracy the temperature dependence of the zero-field susceptibility of antiferromagnets chi with maximum al T le ss than or similar to \J(0)\/D (J(0) is the Fourier component of the e xchange interaction) and describes for the first time the singular beh avior 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)\).