Spin-pair correlations of the classical Heisenberg ferromagnet above and below the critical point: Results of self-consistent Monte Carlo calculations

Abstract

The spin-pair correlation functions of the classical Heisenberg ferromagnet with simple cubic lattice have been calculated in the paramagnetic and ferromagnetic temperature range using the self-consistent Monte Carlo method. The results agree with high-temperature series expansions above Tc, for low temperatures with spin-wave theory. By two different approaches the divergence of the ferromagnetic homogeneous susceptibility in zero field throughout the ferromagnetic temperature range could be verified. The functional dependence of the static susceptibility χT(k) upon the inverse correlation length κ1 is discussed above and below Tc and a Fourier transform for the explicit dependence of the spin correlations upon correlation length below Tc is given. According to these results the scaling assumption v=v′ for the exponents of the correlation length in the critical region is consistent with a divergent ferromagnetic susceptibility. © 1974 Springer-Verlag.