The Heisenberg model for the Hamiltonian of a ferromagnet is given by: $$H=-\frac{J}{2} \sum \vec{S}_i\cdot \vec{S}_j+\mu_B B \sum_i S^z_i$$ when performing mean field theory, to find $\chi$, we assume that the Ising model holds, i.e. take a Hamiltonian to be:
$$H=-\frac{J}{2} \sum S^z_i S^z_j+\mu_B B \sum_i S^z_i$$
My question is why when using mean field theory is it applicable to use the Ising model?
