 Spin-state population and net polarization

For moment projections $\pm \mu$, $p_{+}=(1+\tanh x)/2$ but $M/M_s=\tanh x$, with $x=\mu B/(k_{B}T)$. At zero field half the moments occupy each projection while the net magnetization is zero. An effective Curie moment is also distinct from the saturated projection used in this two-state model.