Spin-state population and net polarization (source code)

= Spin-state population and net polarization
{title2=$p_+=(1+M/M_s)/2$}

For moment projections $\pm\mu$, $p_+=(1+\tanh x)/2$ but $M/M_s=\tanh x$, with $x=\mu B/(k_BT)$. 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.