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The 1/D Expansion for Classical Magnets: Low-Dimensional Models with Magnetic Field
The field-dependent magnetization m(H,T) of 1- and 2-dimensional classical
magnets described by the -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 1-st order in 1/D the theory reproduces with a good accuracy
the 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 the
exchange 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|)