The 1/D expansion for low-dimensional classical magnets

The physical characteristics of two-dimensional classical ferro- and antiferro-magnets have been calculated in the whole temperature range by an analytical approach based on the expansion in powers of 1/D, whereD is the number of spin components. This approach works rather well since it yields exact results for antiferromagnetic susceptibility and specific heat atT=0 already in the first order in 1/D and it is consistent with HTSE at high temperatures. For the quantities singular atT=0, such as ferromagnetic susceptibility and correlation length, the 1/D expansion supports their general-D functional form in the low-temperature range obtained by Fukugita and Oyanagi. The critical index calculated in the first order in 1/D proves to be temperature dependent: =20/(D) (=T/T_c^(MFT),T_c^(MFT)=J₀/D, J₀ is the zero Fourier component of the exchange interaction).